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@incollection{MR2185446,
	Address = {La Jolla, CA},
	Author = {Simpson, Stephen G.},
	Booktitle = {Reverse mathematics 2001},
	Date-Added = {2007-09-27 13:26:49 -0400},
	Date-Modified = {2007-09-27 13:26:49 -0400},
	Mrclass = {03F35 (03B30 03D30 03D80)},
	Mrnumber = {MR2185446 (2006g:03110)},
	Pages = {352--378},
	Publisher = {Assoc. Symbol. Logic},
	Series = {Lect. Notes Log.},
	Title = {{$\Pi\sp 0\sb 1$} sets and models of {$\rm WKL\sb 0$}},
	Volume = {21},
	Year = {2005}}

@article{MR0071379,
	Author = {Myhill, John},
	Date-Added = {2007-09-27 12:59:38 -0400},
	Date-Modified = {2007-09-27 12:59:38 -0400},
	Fjournal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
	Journal = {Z. Math. Logik Grundlagen Math.},
	Mrclass = {02.0X},
	Mrnumber = {MR0071379 (17,118g)},
	Mrreviewer = {J. C. E. Dekker},
	Pages = {97--108},
	Title = {Creative sets},
	Volume = {1},
	Year = {1955}}

@article{MR1640265,
	Author = {Harrington, Leo and Soare, Robert I.},
	Coden = {APALD7},
	Date-Added = {2007-09-27 11:26:09 -0400},
	Date-Modified = {2007-09-27 11:26:09 -0400},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03D25},
	Mrnumber = {MR1640265 (99f:03055)},
	Mrreviewer = {Peter Cholak},
	Note = {Conference on Computability Theory (Oberwolfach, 1996)},
	Number = {1-3},
	Pages = {97--125},
	Title = {Definable properties of the computably enumerable sets},
	Volume = {94},
	Year = {1998}}

@article{MR2210058,
	Author = {Binns, Stephen and Kjos-Hanssen, Bj{\o}rn and Lerman, Manuel and Solomon, Reed},
	Coden = {JSYLA6},
	Date-Added = {2007-09-27 09:17:49 -0400},
	Date-Modified = {2007-09-27 09:17:49 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D28 (28A12)},
	Mrnumber = {MR2210058 (2006m:03070)},
	Mrreviewer = {A. Ku{\v{c}}era},
	Number = {1},
	Pages = {119--136},
	Title = {On a conjecture of {D}obrinen and {S}impson concerning almost everywhere domination},
	Volume = {71},
	Year = {2006}}

@unpublished{Aharoni.Berger:nd,
	Author = {Aharoni, R. and Berger, E.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:05:14 -0400},
	Note = {Draft available},
	Title = {Menger's theorem for infinite graphs},
	Url = {www.math.haifa.ac.il/berger/Menger.ps},
	Year = {2006}}

@article{Federson2002,
	Author = {Federson, M. and Bianconi, R.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Journal = {Journal of Applied Analysis},
	Local-Url = {file://localhost/Users/swalsh/Documents/Sean/Library/Federson2002.pdf},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR1921473}{MR1921473}. \href{http:/www.emis.de/MATH-item?1043.45010}{Zbl 1043.45010}.},
	Number = {1},
	Pages = {83-110},
	Title = {Linear {F}redholm {I}ntegral {E}quations and the {I}ntegral of {K}urzweil},
	Volume = {8},
	Year = {2002}}

@unpublished{Hirschfeldt.Jockusch.ea:nd,
	Author = {Hirschfeldt, D. and Jockusch, C. and Kjos-Hannssen, B. and Lempp, S. and Slaman, T.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Note = {To appear in the preceedings of the Program on Computational Prospects of Infinity, Singapore},
	Title = {Some Remarks on the Proof-theoretic Strength of Some Combinatorial Principles},
	Year = {2005}}

@article{DoughertyKechris1991,
	Author = {Dougherty, Randall and Kechris, Alexander S.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Journal = {Advances in Mathematics},
	Keywords = {Mathematics},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR1120611}{MR1120611}. \href{http:/www.emis.de/MATH-item?0739.26005}{Zbl 0739.26005}.},
	Number = {2},
	Pages = {145-169},
	Title = {The {C}omplexity of {A}ntidifferentiation},
	Volume = {88},
	Year = {1991}}

@unpublished{kjos-hanssen:_low_ness_notion_measur_and_domin,
	Author = {B. Kjos-Hanssen and J. Miller and D. Solomon},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:19:34 -0400},
	Note = {Preprint available from authors},
	Title = {Low- ness notions, measure and domination},
	Year = {2007}}

@unpublished{LMSV:nd,
	Author = {Bienvenu, L. and A. Muchnik and A. Shen and N. Vereshchagin},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:05:32 -0400},
	Note = {Draft available from authors},
	Title = {Limit Complexities Revisited},
	Year = {2007}}

@unpublished{Hirschfeldt.Shore:nd,
	Author = {Hirschfeldt, Denis R. and Shore, Richard A. and Slaman, T.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:10:35 -0400},
	Note = {Draft available from authors},
	Title = {The Atomic Model Theorem},
	Url = {http://www.math.cornell.edu/~shore/papers/pdf/amtnew5.pdf},
	Year = {2007}}

@article{MR2298478,
	Author = {Hirschfeldt, Denis R. and Shore, Richard A.},
	Coden = {JSYLA6},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03F35 (03B30)},
	Mrnumber = {MR2298478},
	Mrreviewer = {Roman Kossak},
	Number = {1},
	Pages = {171--206},
	Title = {Combinatorial principles weaker than {R}amsey's theorem for pairs},
	Volume = {72},
	Year = {2007}}

@unpublished{Eleftheriou1,
	Author = {P. Eleftheriou and S. Starchenko},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Note = {to appear in Journal of Symbolic Logic},
	Title = {Groups definable in ordered vector spaces over ordered division rings},
	Year = {2007}}

@unpublished{Slaman.Woodin:conjecture,
	Author = {Theodore A. Slaman and W. Hugh Woodin},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 14:39:38 -0400},
	Note = {Personal communication},
	Title = {Slaman-{W}oodin Conjecture},
	Year = {1989}}

@unpublished{Avigad:02,
	Author = {Avigad, J.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:09 -0400},
	Note = {Carnegie Mellon Technical Report CMU-PHIL-125},
	Title = {Notes on ${\Pi}^1_1$ conservativity, $\omega$-models, and the collection shema},
	Url = {http://www.andrew.cmu.edu/user/avigad/Papers/omegasubmodels.pdf},
	Year = {2002}}

@incollection{MR1057822,
	Address = {Providence, RI},
	Author = {Hirst, Jeffry L.},
	Booktitle = {Logic and computation (Pittsburgh, PA, 1987)},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Mrclass = {03F35},
	Mrnumber = {MR1057822 (91k:03141)},
	Mrreviewer = {P. {\v{S}}t{\v{e}}p{\'a}nek},
	Pages = {181--196},
	Publisher = {Amer. Math. Soc.},
	Series = {Contemp. Math.},
	Title = {Marriage theorems and reverse mathematics},
	Volume = {106},
	Year = {1990}}

@article{jockusch:72,
	Author = {Jockusch, Jr., Carl G.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Journal = {J. Symbolic Logic},
	Pages = {268--280},
	Title = {Ramsey's theorem and recursion theory},
	Volume = {37},
	Year = {1972}}

@unpublished{kjos-hanssen:_low_for_random_reals_and,
	Author = {B. Kjos-Hanssen},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:19:26 -0400},
	Note = {to appear in Proceedings of the American Mathematical Society,},
	Title = {Low for random reals and positive-measure domination},
	Year = {2005}}

@book{Kress1999,
	Author = {Kress, Rainer},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Edition = {second},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR1723850}{MR1723850}. \href{http:/www.emis.de/MATH-item?0920.45001}{Zbl 0920.45001}.},
	Publisher = {Springer},
	Series = {Applied Mathematical Sciences},
	Title = {Linear {I}ntegral {E}quations},
	Volume = {82},
	Year = {1999}}

@book{Kurzweil2000,
	Address = {Singapore},
	Author = {Kurzweil, Jaroslav},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Keywords = {Mathematics},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR1763305}{MR1763305}. \href{http:/www.emis.de/MATH-item?0954.28001}{Zbl 0954.28001}.},
	Publisher = {World Scientific},
	Series = {Series in Real Analysis},
	Title = {Henstock-{K}urzweil {I}ntegration: {I}ts {R}elation to {T}opological {V}ector {S}paces},
	Volume = {7},
	Year = {2000}}

@phdthesis{Mileti:04,
	Author = {J. Mileti},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	School = {University of Illinios at Urbana-Champaign},
	Title = {Partition Theorems and Computbility Theory},
	Year = {2004}}

@unpublished{miller:nd,
	Author = {J. Miller},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:12:01 -0400},
	Note = {Talk at FRG Workshop September 15-19, 2007},
	Title = {Extracting information is hard},
	Year = {2007}}

@article{miller:01,
	Author = {Miller, Russell},
	Coden = {JSYLA6},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D45},
	Mrnumber = {2002e:03065},
	Mrreviewer = {Peter Cholak},
	Number = {2},
	Pages = {470--486},
	Title = {The ${\Delta}\sp 0\sb 2$-spectrum of a linear order},
	Volume = {66},
	Year = {2001}}

@book{Prest1988,
	Address = {Cambridge},
	Author = {Prest, Mike},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR933092}{MR933092}. \href{http:/www.emis.de/MATH-item?0634.03025}{Zbl 0634.03025}.},
	Publisher = {Cambridge University Press},
	Series = {London Mathematical Society Lecture Note Series},
	Title = {Model {T}heory and {M}odules},
	Volume = {130},
	Year = {1988}}

@unpublished{Reimann:nd,
	Author = {Jan Reimann},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:11:37 -0400},
	Note = {Submitted},
	Title = {Randomness beyond Lebesgue measure},
	Url = {http://math.berkeley.edu/~reimann/Publications/randomness_beyond_preprint.pdf},
	Year = {2007}}

@book{Saks1937,
	Address = {New York},
	Author = {Saks, Stanis{\l}aw},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Note = {With two additional notes by Stefan Banach. Translated by L.C. Young. \href{http://www.ams.org/mathscinet-getitem?mr=MR0167578}{MR0167578}. \href{http:/www.emis.de/MATH-item?63.0183.05}{JFM 63.0183.05}.},
	Publisher = {Stechert},
	Series = {Monografie Matematyczne},
	Title = {Theory of the {I}ntegral},
	Volume = {7},
	Year = {1937}}

@book{samuel:70,
	Address = {Boston, Mass.},
	Author = {Samuel, Pierre},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Mrclass = {10.01},
	Mrnumber = {42 \#177},
	Pages = {109},
	Publisher = {Houghton Mifflin Co.},
	Title = {Algebraic theory of numbers},
	Year = {1970}}

@article{MR929498,
	Author = {Shelah, Saharon},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Fjournal = {Journal of the American Mathematical Society},
	Issn = {0894-0347},
	Journal = {J. Amer. Math. Soc.},
	Mrclass = {05A17 (03D20)},
	Mrnumber = {MR929498 (89a:05017)},
	Mrreviewer = {Andreas Blass},
	Number = {3},
	Pages = {683--697},
	Title = {Primitive recursive bounds for van der {W}aerden numbers},
	Volume = {1},
	Year = {1988}}

@unpublished{simpson2,
	Author = {Steve Simpson},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 13:27:12 -0400},
	Note = {to appear in Mathematical Logic Quarterly},
	Title = {Almost everywhere domination and superhighness},
	Year = {2006}}

@book{Swartz2001,
	Address = {Singapore},
	Author = {Swartz, Charles},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Keywords = {Mathematics},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR1845270}{MR1845270}. \href{http:/www.emis.de/MATH-item?0982.26006}{Zbl 0982.26006}.},
	Publisher = {World Scientific},
	Title = {Introduction to {G}auge {I}ntegrals},
	Year = {2001}}

@article{MR0369312,
	Author = {Szemer{\'e}di, E.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	Fjournal = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
	Issn = {0065-1036},
	Journal = {Acta Arith.},
	Mrclass = {10L10},
	Mrnumber = {MR0369312 (51 \#5547)},
	Mrreviewer = {S. L. G. Choi},
	Note = {Collection of articles in memory of Juri\u\i\ Vladimirovi\v c Linnik},
	Pages = {199--245},
	Title = {On sets of integers containing no {$k$} elements in arithmetic progression},
	Volume = {27},
	Year = {1975}}

@unpublished{tao:nd,
	Author = {Tao, T.},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 09:12:19 -0400},
	Note = {to appear, ICM 2006 proceedings.},
	Title = {The dichotomy between structure and randomness, arithmetic progressions,},
	Year = {2006}}

@phdthesis{walk:99,
	Author = {Stephen M. Walk},
	Date-Added = {2007-09-27 08:22:09 -0400},
	Date-Modified = {2007-09-27 08:22:10 -0400},
	School = {University of Notre Dame},
	Title = {Toward the definability of the array noncomputable degrees},
	Year = 1999}

@unpublished{K,
	Author = {J. Knight},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:42 -0400},
	Note = {in preparation},
	Title = {A computable structure of Scott rank $\omega_1^{CK}$ whose computable infinitary theory is not $\aleph_0$-categorical}}

@article{Hjorth1,
	Author = {Greg Hjorth},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:42 -0400},
	Journal = {Notre Dame J. Formal Logic},
	Number = {1},
	Pages = {49-51},
	Title = {A Note on Counterexamples to the Vaught Conjecture},
	Volume = {48},
	Year = {2007}}

@article{MR1987431,
	Author = {Binns, Stephen},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:42 -0400},
	Fjournal = {MLQ. Mathematical Logic Quarterly},
	Issn = {0942-5616},
	Journal = {MLQ Math. Log. Q.},
	Mrclass = {03D30},
	Mrnumber = {MR1987431 (2004f:03079)},
	Mrreviewer = {Peter Cholak},
	Number = {4},
	Pages = {327--335},
	Title = {A splitting theorem for the {M}edvedev and {M}uchnik lattices},
	Volume = {49},
	Year = {2003}}

@article{tric,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Coden = {PLMTAL},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:43 -0400},
	Fjournal = {Proceedings of the London Mathematical Society. Third Series},
	Issn = {0024-6115},
	Journal = {Proc. London Math. Soc. (3)},
	Mrclass = {03C45 (03C40 03C60 12L12)},
	Mrnumber = {MR1643405 (2000b:03123)},
	Mrreviewer = {O. V. Belegradek},
	Number = {3},
	Pages = {481--523},
	Title = {A trichotomy theorem for o-minimal structures},
	Volume = {77},
	Year = {1998}}

@unpublished{rodenisbook,
	Author = {Rod Downey and Denis R. Hirschfeldt},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:43 -0400},
	Note = {Draft available.},
	Title = {Algorithmic Randomness and Complexity}}

@article{Axon4p,
	Author = {Barmpalias, George and Broadhead, Paul and Cenzer, Douglas and Dashti, Seyyed and Weber, Rebecca},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:43 -0400},
	Journal = {Journal for Logic and Computation},
	Title = {Algorithmic Randomness of Closed Sets},
	Year = {to appear}}

@article{MR2078930,
	Author = {Dobrinen, Natasha L. and Simpson, Stephen G.},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:43 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D28 (03B30 03F35 28A05 28E15)},
	Mrnumber = {2005d:03079},
	Mrreviewer = {Denis R. Hirschfeldt},
	Number = {3},
	Pages = {914--922},
	Title = {Almost everywhere domination},
	Volume = {69},
	Year = {2004}}

@article{M,
	Author = {Makkai, M.},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:43 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03C70},
	Mrnumber = {MR613284 (82m:03049)},
	Mrreviewer = {Bienvenido F. Nebres},
	Number = {2},
	Pages = {301--318},
	Title = {An example concerning {S}cott heights},
	Volume = {46},
	Year = {1981}}

@book{Kaplansky1976,
	Address = {Paris},
	Author = {Kaplansky, Irving},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:44 -0400},
	Edition = {Second},
	Keywords = {Mathematics},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR0460303}{MR0460303}. \href{http:/www.emis.de/MATH-item?0954.12500 }{Zbl 0954.12500}.},
	Number = {1251},
	Publisher = {Hermann},
	Series = {Actualit\'es Scientifiques et Industrielles},
	Title = {An {I}ntroduction to {D}ifferential {A}lgebra},
	Year = {1976}}

@article{MR831773,
	Author = {Asarin, E. A. and Pokrovski{\u\i}, A. V.},
	Coden = {AVTEAI},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:44 -0400},
	Fjournal = {Akademiya Nauk SSSR. Avtomatika i Telemekhanika},
	Issn = {0005-2310},
	Journal = {Avtomat. i Telemekh.},
	Mrclass = {93E03},
	Mrnumber = {MR831773 (87e:93096)},
	Number = {1},
	Pages = {25--33},
	Title = {Application of {K}olmogorov complexity to the analysis of the dynamics of controllable systems},
	Year = {1986}}

@article{MR1782129,
	Author = {Fouch{\'e}, Willem},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:44 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {68Q30 (03D15 60J65)},
	Mrnumber = {MR1782129 (2002b:68038)},
	Mrreviewer = {Andreas Blass},
	Number = {1},
	Pages = {421--442},
	Title = {Arithmetical representations of {B}rownian motion. {I}},
	Volume = {65},
	Year = {2000}}

@unpublished{MS,
	Author = {J. Millar andd G. Sacks},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:44 -0400},
	Note = {preprint},
	Title = {Atomic models higher up}}

@article{Soare:74*1,
	Author = {Soare, Robert I.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:45 -0400},
	Journal = {Bull. Amer. Math. Soc.},
	Mrclass = {02F25},
	Mrnumber = {MR0373858 (51 \#10058)},
	Mrreviewer = {Manuel Lerman},
	Pages = {53--58},
	Title = {Automorphisms of the lattice of recursively enumerable sets},
	Volume = {80},
	Year = {1974}}

@unpublished{CGK2,
	Author = {W. Calvert and J. Knight and S.Goncharov},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:45 -0400},
	Note = {in preparation},
	Title = {Boolean algebras and rank preservation}}

@article{MR2248591,
	Author = {Downey, Rod and Hirschfeldt, Denis R. and Nies, Andr{\'e} and Terwijn, Sebastiaan A.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:45 -0400},
	Fjournal = {The Bulletin of Symbolic Logic},
	Issn = {1079-8986},
	Journal = {Bull. Symbolic Logic},
	Mrclass = {03D80 (60A05 68Q30)},
	Mrnumber = {MR2248591},
	Number = {3},
	Pages = {411--491},
	Title = {Calibrating randomness},
	Volume = {12},
	Year = {2006}}

@unpublished{CGKM,
	Author = {W. Calvert and J. Knight and S. Goncharov and J. Millar},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:45 -0400},
	Note = {in preparation},
	Title = {Categorical computable infinitary theories}}

@unpublished{HJK,
	Author = {V. Harizanov and J. Knight and Carl Jockusch},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:45 -0400},
	Note = {in preparation},
	Title = {Chains and anti-chains in partial orders}}

@phdthesis{walkerwhite:00,
	Address = {Ithaca, NY, USA},
	Author = {Walker M. White},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	School = {Cornell University},
	Title = {Characterizations for Computable Structures},
	Year = 2000}

@article{CK,
	Author = {W. Calvert and J. Knight},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	Journal = {Bull. Symbolic Logic},
	Note = {Solicited expository paper},
	Number = {191-218},
	Title = {Classification from a computable point of view},
	Volume = {12},
	Year = {2006}}

@incollection{DK,
	Address = {Providence, RI},
	Author = {D'Aquino, Paola and Knight, Julia F.},
	Booktitle = {Nonstandard models of arithmetic and set theory},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	Mrclass = {03H15 (03C62)},
	Mrnumber = {MR2089274 (2005h:03126)},
	Mrreviewer = {Constantine Dimitracopoulos},
	Pages = {23--36},
	Publisher = {Amer. Math. Soc.},
	Series = {Contemp. Math.},
	Title = {Coding in {$I\Delta\sb 0$}},
	Volume = {361},
	Year = {2004}}

@phdthesis{Hirst:87,
	Author = {Hirst, Jeffry L.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	School = {The Pennsylvania State University},
	Title = {Combinatorics in {S}ubsystems of {S}econd {O}rder {A}rithmetic},
	Year = {1987}}

@unpublished{el2,
	Author = {Pantelis Eleftheriou},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	Note = {Submitted, preprint available},
	Title = {Compact domination for groups definable in linear o-minimal structures},
	Year = {2006}}

@article{MR2135656,
	Author = {Ambos-Spies, Klaus and Kjos-Hanssen, Bj{\o}rn and Lempp, Steffen and Slaman, Theodore A.},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:46 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D28 (03F35 03F60)},
	Mrnumber = {MR2135656},
	Number = {4},
	Pages = {1089--1104},
	Title = {Comparing {DNR} and {WWKL}},
	Volume = {69},
	Year = {2004}}

@article{CCKM,
	Author = {Calvert, Wesley and Cummins, D. and Julia Knight and Miller, S.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:47 -0400},
	Fjournal = {Algebra i Logika. Institut Diskretno\u\i\ Matematiki i Informatiki},
	Issn = {0373-9252},
	Journal = {Algebra Logika},
	Mrclass = {03C57 (03C13 03C15 03D45)},
	Mrnumber = {MR2135387 (2006e:03049)},
	Mrreviewer = {Andrey Morozov},
	Number = {6},
	Pages = {666--701, 759},
	Title = {Comparison of classes of finite structures},
	Volume = {43},
	Year = {2004}}

@unpublished{crele,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:47 -0400},
	Note = {submitted, preprint available},
	Title = {Complex analytic geometry and analytic-geometric categories},
	Year = {2006}}

@unpublished{newtonan,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:47 -0400},
	Note = {to appear in the Special Volume of Isaak Newton Institute},
	Title = {Complex analytic geometry in non-standard setting},
	Year = {2006}}

@article{MR2136634,
	Author = {Soare, Robert I.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:47 -0400},
	Fjournal = {The Bulletin of Symbolic Logic},
	Issn = {1079-8986},
	Journal = {Bull. Symbolic Logic},
	Mrclass = {03D25 (03D10 53C23)},
	Mrnumber = {MR2136634 (2005m:03084)},
	Number = {4},
	Pages = {457--486},
	Title = {Computability theory and differential geometry},
	Volume = {10},
	Year = {2004}}

@unpublished{ChKM2,
	Author = {J. Chisholm and J. Knight and S. Miller},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:47 -0400},
	Note = {to appear in J.\ Symb. Logic},
	Title = {Computable embeddings and strongly minimal theories}}

@unpublished{HKLMMMW,
	Author = {V. Harizanov and J. Knight and Karen Lange and C. Maher and S. Miller and C. McCoy and J. Wallbaum},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Note = {in preparation},
	Title = {Computable fields}}

@unpublished{GrK,
	Author = {Noam Greenberg and J. Knight},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Note = {in preparation},
	Title = {Computable structure theory on $\omega_1$}}

@book{MR1767842,
	Address = {Amsterdam},
	Author = {Ash, C. J. and Knight, J.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Isbn = {0-444-50072-3},
	Mrclass = {03D45 (03-02 03D28 03D30)},
	Mrnumber = {MR1767842},
	Mrreviewer = {Rodney G. Downey},
	Pages = {xvi+346},
	Publisher = {North-Holland Publishing Co.},
	Series = {Studies in Logic and the Foundations of Mathematics},
	Title = {Computable structures and the hyperarithmetical hierarchy},
	Volume = {144},
	Year = {2000}}

@inbook{CGK,
	Author = {W. Calvert and S. Goncharov and J. Knight},
	Booktitle = {Advances in Logic},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Editor = {Gao and Jackson and Zhang},
	Pages = {43-66},
	Publisher = {AMS},
	Series = {Con.\ Math},
	Title = {Computable structures of Scott rank $\omega_1^{CK}$ in familiar classes},
	Year = {2007}}

@article{MR2210068,
	Author = {Calvert, Wesley and Knight, Julia F. and Millar, Jessica},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D45 (03C75)},
	Mrnumber = {MR2210068},
	Number = {1},
	Pages = {283--298},
	Title = {Computable trees of {S}cott rank {$\omega\sb 1\sp {CK}$}, and computable approximation},
	Volume = {71},
	Year = {2006}}

@article{CKM,
	Author = {W. Calvert and J. Knight and J. Millar},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:48 -0400},
	Journal = {J. Symbolic Logic},
	Number = {283-298},
	Title = {Computable trees of Scott rank $\omega_1^{CK}$, and computable approximation},
	Volume = {71},
	Year = {2006}}

@article{pps1,
	Author = {Peterzil, Y. and Pillay, A. and Starchenko, S.},
	Coden = {TAMTAM},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:49 -0400},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {03C60 (03C64 20A15)},
	Mrnumber = {MR1707202 (2001b:03036)},
	Mrreviewer = {H. Dugald Macpherson},
	Number = {10},
	Pages = {4397--4419},
	Title = {Definably simple groups in o-minimal structures},
	Volume = {352},
	Year = {2000}}

@phdthesis{kautz,
	Author = {Steven Kautz},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:49 -0400},
	School = {Cornell University},
	Title = {Degrees of Random Sets},
	Year = {1991}}

@article{MR2001061,
	Author = {Cenzer, Douglas and Hinman, Peter G.},
	Coden = {AMLOEH},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:49 -0400},
	Fjournal = {Archive for Mathematical Logic},
	Issn = {0933-5846},
	Journal = {Arch. Math. Logic},
	Mrclass = {03D30 (03D65)},
	Mrnumber = {MR2001061 (2004k:03081)},
	Mrreviewer = {C. G. Jockusch, Jr.},
	Number = {6},
	Pages = {583--600},
	Title = {Density of the {M}edvedev lattice of {$\Pi\sp 0\sb 1$} classes},
	Volume = {42},
	Year = {2003}}

@book{Cohn1965,
	Address = {New York},
	Author = {Cohn, Richard M.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:49 -0400},
	Note = {\href{http://www.ams.org/mathscinet-getitem?mr=MR0205987}{MR0205987}. \href{http:/www.emis.de/MATH-item?0127.26402}{Zbl 0127.26402}.},
	Publisher = {Interscience},
	Title = {Difference {A}lgebra},
	Year = {1965}}

@article{CCHM,
	Author = {Calvert, Wesley and Cenzer, Douglas and Harizanov, Valentina and Morozov, Andrei},
	Coden = {APALD7},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:49 -0400},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03C57 (03D45)},
	Mrnumber = {MR2229930},
	Number = {1-2},
	Pages = {61--78},
	Title = {Effective categoricity of equivalence structures},
	Volume = {141},
	Year = {2006}}

@unpublished{Co,
	Author = {Joshua A. Cole},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:50 -0400},
	Note = {Submitted},
	Title = {Embedding $FD(\omega)$ into $\mathcal{P}_s$ densely},
	Year = {2007}}

@article{MR2052891,
	Author = {Binns, Stephen and Simpson, Stephen G.},
	Coden = {AMLOEH},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:50 -0400},
	Fjournal = {Archive for Mathematical Logic},
	Issn = {0933-5846},
	Journal = {Arch. Math. Logic},
	Mrclass = {03D30},
	Mrnumber = {MR2052891 (2004m:03156)},
	Mrreviewer = {Peter Cholak},
	Number = {3},
	Pages = {399--414},
	Title = {Embeddings into the {M}edvedev and {M}uchnik lattices of {$\Pi\sp 0\sb 1$} classes},
	Volume = {43},
	Year = {2004}}

@article{GHKMMS,
	Author = {Goncharov, Sergey and Harizanov, Valentina and Knight, Julia and McCoy, Charles and Miller, Russell and Solomon, Reed},
	Coden = {APALD7},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:50 -0400},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03D45 (03C57)},
	Mrnumber = {MR2169684 (2006f:03071)},
	Mrreviewer = {Denis R. Hirschfeldt},
	Number = {3},
	Pages = {219--246},
	Title = {Enumerations in computable structure theory},
	Volume = {136},
	Year = {2005}}

@article{MR2275865,
	Author = {Csima, Barbara F. and Downey, Rod and Greenberg, Noam and Hirschfeldt, Denis R. and Miller, Joseph S.},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:50 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D80 (03D28)},
	Mrnumber = {MR2275865},
	Mrreviewer = {Liang Yu},
	Number = {4},
	Pages = {1385--1393},
	Title = {Every 1-generic computes a properly 1-generic},
	Volume = {71},
	Year = {2006}}

@article{ps1,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Coden = {SMATF6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:50 -0400},
	Fjournal = {Selecta Mathematica. New Series},
	Issn = {1022-1824},
	Journal = {Selecta Math. (N.S.)},
	Mrclass = {03C64 (12J15 12L12 30C35)},
	Mrnumber = {MR1868299 (2002m:03056)},
	Mrreviewer = {G. Cherlin},
	Number = {3},
	Pages = {409--445},
	Title = {Expansions of algebraically closed fields in o-minimal structures},
	Volume = {7},
	Year = {2001}}

@article{ps2,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:51 -0400},
	Fjournal = {Journal of Mathematical Logic},
	Issn = {0219-0613},
	Journal = {J. Math. Log.},
	Mrclass = {03C64 (03H05 12J15 12L12)},
	Mrnumber = {MR1978941 (2004f:03072)},
	Mrreviewer = {Christopher L. Miller},
	Number = {1},
	Pages = {1--35},
	Title = {Expansions of algebraically closed fields. {II}. {F}unctions of several variables},
	Volume = {3},
	Year = {2003}}

@article{Lippelpaper,
	Author = {Lippel, David},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:51 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03C45 (03C35 18C50)},
	Mrnumber = {MR2140041 (2005m:03058)},
	Mrreviewer = {Alexandre Ivanov},
	Number = {2},
	Pages = {460--472},
	Title = {Finitely axiomatizable {$\omega$}-categorical theories and the {M}azoyer hypothesis},
	Volume = {70},
	Year = {2005}}

@book{MR0265324,
	Address = {South Bend, Ind.},
	Author = {Artin, Emil},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:51 -0400},
	Mrclass = {12.40},
	Mrnumber = {MR0265324 (42 \#234)},
	Pages = {iii+82},
	Publisher = {University of Notre Dame Press},
	Series = {Edited and supplemented with a section on applications by Arthur N. Milgram. Second edition, with additions and revisions. Fifth reprinting. Notre Dame Mathematical Lectures, No. 2},
	Title = {Galois theory},
	Year = {1959}}

@article{geocalc,
	Author = {Peterzil, Ya'acov and Starchenko, Sergei},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:52 -0400},
	Fjournal = {The Bulletin of Symbolic Logic},
	Issn = {1079-8986},
	Journal = {Bull. Symbolic Logic},
	Mrclass = {03C45},
	Mrnumber = {MR1380825 (97d:03045)},
	Mrreviewer = {Bruno Poizat},
	Number = {1},
	Pages = {72--83},
	Title = {Geometry, calculus and {Z}ilber's conjecture},
	Volume = {2},
	Year = {1996}}

@unpublished{el1,
	Author = {Pantelis Eleftheriou},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:52 -0400},
	Note = {Submitted, preprint available},
	Title = {Groups definable in linear o-minimal structures},
	Year = {2006}}

@incollection{MR1640327,
	Address = {Amsterdam},
	Author = {Fairtlough, Matt and Wainer, Stanley S.},
	Booktitle = {Handbook of proof theory},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:52 -0400},
	Mrclass = {03D20 (03F30)},
	Mrnumber = {MR1640327 (2000a:03063)},
	Mrreviewer = {Alessandro Berarducci},
	Pages = {149--207},
	Publisher = {North-Holland},
	Series = {Stud. Logic Found. Math.},
	Title = {Hierarchies of provably recursive functions},
	Volume = {137},
	Year = {1998}}

@unpublished{CFGKKMP,
	Author = {W. Calvert and E. Fokina and S. Goncharov and J. Knight and O. Kudinov and A. S. Morosov and V. Puzarenko},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:53 -0400},
	Note = {to appear in J.\ Symb. Logic},
	Title = {Index sets for classes of high rank structures}}

@article{CHKM,
	Author = {W. Calvert and V. Harizanov and J. Knight and S. Miller},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:53 -0400},
	Journal = {Algebra and Logic},
	Pages = {306-325},
	Title = {Index sets for computable structures},
	Volume = {45},
	Year = {2006}}

@unpublished{ChFGHKM,
	Author = {J. Chisholm and E. Fokina and S. Goncharov and J. Knight and S. Miller},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:53 -0400},
	Note = {preprint},
	Title = {Intrinsic bounds on complexity at limit levels}}

@article{Weber:06,
	Author = {Weber, Rebecca},
	Coden = {TAMTAM},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:53 -0400},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {03D28 (03D25)},
	Mrnumber = {MR2216257 (2006k:03076)},
	Mrreviewer = {Steffen Lempp},
	Number = {7},
	Pages = {3023--3059 (electronic)},
	Title = {Invariance in {$\mathcal{E}^*$} and {$\mathcal{E}_{\Pi}$}},
	Volume = {358},
	Year = {2006}}

@unpublished{kaneb,
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:54 -0400},
	Title = {Kaneb Center},
	Url = {http://kaneb.nd.edu/ta/}}

@article{MR2251554,
	Author = {Downey, Rod and Nies, Andre and Weber, Rebecca and Yu, Liang},
	Coden = {JSYLA6},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:54 -0400},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Mrclass = {03D80 (68Q30)},
	Mrnumber = {MR2251554},
	Number = {3},
	Pages = {1044--1052},
	Title = {Lowness and {$\Pi\sp 0\sb 2$} nullsets},
	Volume = {71},
	Year = {2006}}

@article{MR2166184,
	Author = {Nies, Andr{\'e}},
	Coden = {ADMTA4},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:54 -0400},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {68Q30 (03D28)},
	Mrnumber = {MR2166184 (2006j:68052)},
	Mrreviewer = {Joseph S. Miller},
	Number = {1},
	Pages = {274--305},
	Title = {Lowness properties and randomness},
	Volume = {197},
	Year = {2005}}

@unpublished{simpson1,
	Author = {Stephen G. Simpson},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:55 -0400},
	Note = {to appear in Mathematical Logic Quarterly},
	Title = {Mass Problems and Almost Everywhere Domination},
	Year = {2006}}

@unpublished{CoSi,
	Author = {Joshua A. Cole and Stephen G. Simpson},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:55 -0400},
	Note = {Submitted},
	Title = {Mass Problems and Hyperarithmeticity},
	Year = {2006}}

@article{MR2125147,
	Author = {Simpson, Stephen G.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:55 -0400},
	Fjournal = {The Bulletin of Symbolic Logic},
	Issn = {1079-8986},
	Journal = {Bull. Symbolic Logic},
	Mrclass = {03D30 (03D25 03D80 03F15 03F35 68Q30)},
	Mrnumber = {2125147},
	Number = {1},
	Pages = {1--27},
	Title = {Mass problems and randomness},
	Volume = {11},
	Year = {2005}}

@book{O,
	Address = {New York},
	Author = {Oxtoby, John C.},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:55 -0400},
	Edition = {Second},
	Isbn = {0-387-90508-1},
	Mrclass = {28-02 (54H99)},
	Mrnumber = {MR584443 (81j:28003)},
	Note = {A survey of the analogies between topological and measure spaces},
	Pages = {x+106},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Measure and category},
	Volume = {2},
	Year = {1980}}

@article{MR2250550,
	Author = {Fuchino, Sakae and Greenberg, Noam and Shelah, Saharon},
	Coden = {APALD7},
	Date-Added = {2007-05-17 11:14:42 -0400},
	Date-Modified = {2007-05-17 11:14:55 -0400},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03E55 (03E35)},
	Mrnumber = {MR2250550 (2007d:03091)},
	Mrreviewer = {Stefan Geschke},
	Number = {1-3},
	Pages = {380--397},
	Title = {Models of real-valued measurability},
	Volume = {142},
	Year = {2006}}

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@article{d-vdd,
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@article{MR2058190,
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@article{GHKS,
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@book{MR0385969,
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@unpublished{greenberg1,
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@book{rm2001,
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@unpublished{Downey.Montalban:nd,
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@unpublished{DK2,
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@article{bupiwa:cb,
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@unpublished{teaching,
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@article{MR1794714,
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@unpublished{V,
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@article{MR2017894,
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@inproceedings{Axon2p,
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@unpublished{edel,
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@book{Saks1964,
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@unpublished{CHS,
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@unpublished{Ambos-Spies.Cooper.ea:86,
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@article{Ambos-Spies.Fejer.ea:96,
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	Year = {1996}}

@unpublished{Ambos-Spies.Fejer:02,
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	Note = {To appear},
	Title = {Embedding of $N_5$ and the contiguous degrees},
	Year = {2002}}

@article{Ambos-Spies.Fejer:88,
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	Year = {1988}}

@inproceedings{Ambos-Spies.Homer.ea:90,
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@unpublished{Ambos-Spies.Lempp.ea:91,
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@unpublished{Bickford.Mills:nd,
	Author = {M. Bickford and C.F. Mills},
	Note = {To appear in the JSL (supposedly but no way by this time)},
	Title = {Lowness properties of r.e.\ sets}}

@article{Birkhoff:48,
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	Journal = {Amer. Math. Soc.},
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	Year = {1948}}

@inproceedings{Blass.Hirst.ea:87,
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	Booktitle = {Logic and Combinatorics},
	Pages = {89--124},
	Publisher = {American Mathematical Society},
	Series = {Contemporary Mathematics},
	Title = {Logical Analysis of Some Theorems of Combinatorics and Topological Dynamics},
	Volume = {65},
	Year = {1987}}

@article{Blum.Marques:73,
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	Journal = {J. Symbolic Logic},
	Pages = {579--593},
	Title = {On Computational Complexity of Recursively Enumerable Sets},
	Volume = {38},
	Year = {1973}}

@book{Bollobas:98,
	Address = {New York},
	Author = {Bollob{\'a}s, B{\'e}la},
	Isbn = {0-387-98488-7},
	Mrclass = {05-01 (05-02 05Cxx)},
	Mrnumber = {99h:05001},
	Mrrevr = {Jerrold W. Grossman},
	Pages = {xiv+394},
	Publisher = {Springer-Verlag},
	Title = {Modern graph theory},
	Year = {1998}}

@incollection{Bonnet.Pouzet:82,
	Address = {Dordrecht},
	Author = {Bonnet, R. and Pouzet, M.},
	Booktitle = {Ordered sets (Banff, Alta., 1981)},
	Mrclass = {06A10 (04A10 06A05)},
	Mrnumber = {83h:06004},
	Mrrevr = {Tadashi Ohkuma},
	Pages = {125--170},
	Publisher = {Reidel},
	Title = {Linear extensions of ordered sets},
	Year = {1982}}

@article{Boolos.Putnam:68,
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	Pages = {497--513},
	Title = {Degrees of unsolvability of constructible sets of integers},
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	Year = {1968}}

@article{Boone.Rogers:66,
	Author = {Boone, W. W. and Rogers, Jr. H.},
	Journal = {Math. Scand.},
	Pages = {185-192},
	Title = {On a problem of J.H. C. Whitehead and a problem of Alonzo Church,},
	Volume = {19},
	Year = {1966}}

@article{Boone:66,
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	Journal = {Ann. of Math. (2)},
	Pages = {49-84},
	Title = {Word problems and recursively enumerable degrees of unsolvability, a sequel on finitely presented groups},
	Volume = {84},
	Year = {1966}}

@inproceedings{Brackin:87,
	Author = {S. H. Brackin},
	Booktitle = {Logic and Combinatorics},
	Pages = {169--178},
	Publisher = {American Mathematical Society},
	Series = {Contemporary Mathematics},
	Title = {A Summary of {R}amsey-type Theorems and their Provability in Weak Formal Systems},
	Volume = {65},
	Year = {1987}}

@article{Brown.Simpson:93,
	Author = {Brown, D. K. and Simpson, Stephen G.},
	Journal = {J. Symbolic Logic},
	Key = {Brown-Simpson:BCT},
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	Title = {The {B}aire category theorem in weak subsystems of second-order arithmetic},
	Volume = {58},
	Year = {1993}}

@phdthesis{Brown:87,
	Address = {University Park, PA, USA},
	Author = {Brown, D. K.},
	School = {The Pennsylvania State University},
	Title = {Functional analysis in weak subsystems of second order arithmetic},
	Year = {1987}}

@article{Buchi:60,
	Author = {J. R. B{\"u}chi},
	Journal = {Z. Math. Logik Grundlag. Math.},
	Pages = {66--92},
	Title = {Weak Second Order Arithmetic and Finite Automata},
	Volume = {6},
	Year = {1960}}

@inproceedings{Buchi:62,
	Author = {J. R. B{\"u}chi},
	Booktitle = {Proc. of the International Congress on logic, Math, and Philosophy of Science (1960)},
	Publisher = {Standford University Press},
	Title = {On a decision method in restricted second-order arithmetic},
	Year = {1962}}

@article{Burr:84,
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	Title = {Some undecidable problems involving the edge-coloring and vertex-coloring of graphs},
	Volume = {50},
	Year = {1984}}

@article{Burris.Sankappanavar:75,
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	Journal = {Algebra Universalis},
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	Title = {Lattice theoretic decision problems in universal algebra},
	Volume = {5},
	Year = {1975}}

@book{Burris.Sankappanavar:81,
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	Author = {Burris, S. and Sankappanavar, H. P.},
	Publisher = {Springer--Verlag},
	Title = {A course in universal algebra},
	Year = {1981}}

@article{Calhoun.Slaman:nd,
	Author = {Calhoun, William C. and Slaman, Theodore A.},
	Journal = {J. Symbolic Logic},
	Note = {To appear},
	Title = {The {$\Pi^0_2$} $e$-Degrees are not Dense}}

@article{Calude.Nies:98,
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	Note = {to appear},
	Title = {Chaitin $\Omega$ Numbers and Strong Reducibilities},
	Year = {1998}}

@article{Carlson.Simpson:84,
	Author = {Timothy J. Carlson and Stephen G. Simpson},
	Journal = {Adv. in Math.},
	Pages = {265--290},
	Title = {A Dual Form of {R}amsey's {T}heorem},
	Volume = {53},
	Year = {1984}}

@article{Carstens.Pappinghaus:83,
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	Journal = {Ann. Pure Appl. Logic},
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	Title = {Recursive Coloration of Countable Graphs},
	Volume = {25},
	Year = {1983}}

@inproceedings{Carstens.Pappinghaus:84,
	Address = {Heidelberg},
	Author = {Hans-Georg Carstens and Peter Pappinghaus},
	Booktitle = {Computation and Proof Theory},
	Pages = {39--62},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Abstract Constructions of Counterexamples in Recursive Graph Theory},
	Volume = {1104},
	Year = {1984}}

@incollection{Carstens.Pappinghaus:84*1,
	Address = {Heidelberg},
	Author = {Hans-Georg Carstens and Peter Pappinghaus},
	Booktitle = {Decision Problems and Complexity},
	Editor = {Borger and Hasenjaeger and Rodding},
	Pages = {162--182},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Extensible Algorithms},
	Volume = {171},
	Year = {1984}}

@article{Case.Smith:83,
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	Title = {Comparison of Identification Criteria for Machine Inductive Inference},
	Volume = {25},
	Year = {1983}}

@article{Case:71,
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	Pages = {419--439},
	Title = {Enumeration Reducibility and Partial Degrees},
	Volume = {2},
	Year = {1971}}

@article{Cenzer.Downey.ea:93,
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	Title = {Countable thin $\Pi ^0_1$ clases},
	Volume = {597},
	Year = {1993}}

@book{Chang.Keisler:73,
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	Author = {Chang, C. C. and Keisler, H. J.},
	Publisher = {North--Holland Publishing Co.},
	Title = {Model Theory},
	Year = {1973}}

@article{Chong.Mourad:90,
	Author = {Chong, C.T. and Mourad, K. J.},
	Journal = {Ann. Pure Appl. Logic},
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	Title = {The degree of a $\sum_n$-cut},
	Volume = {48},
	Year = {1990}}

@article{Chong.Mourad:92,
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	Journal = {Trans. Amer. Math. Soc.},
	Pages = {349--363},
	Title = {${\Sigma}_n$ definability without ${\Sigma}_n$ induction},
	Volume = {334},
	Year = {1992}}

@proceedings{Chong:89,
	Author = {Chong, C. T.},
	Editor = {J. Shinoda, T. A. Slaman and T. Tugu\'{e}},
	Number = {1388},
	Pages = {1-16},
	Publisher = {Springer--Verlag},
	Series = {Mathematical Logic and Applications (Proceedings, Kyoto 1987)},
	Title = {Recursively enumerable sets in models of $\sum_2$-collection},
	Year = {1989}}

@article{Church:36,
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	Title = {A note on the {E}ntscheidungsproblem},
	Volume = {1},
	Year = {1936}}

@article{Church:36*1,
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	Journal = {Amer. J. Math.},
	Pages = {345--363},
	Title = {An unsolvable problem of elementary number theory},
	Volume = {58},
	Year = {1936}}

@article{Clapham:64,
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	Pages = {633-676},
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	Volume = {14},
	Year = {1964}}

@inproceedings{Clote:84,
	Address = {Heidelberg},
	Author = {Peter Clote},
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	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Weak partition relations, finite games, and independence results in Peano arithmetic},
	Volume = {834},
	Year = {1984}}

@article{Clote:84*1,
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	Pages = {376--400},
	Title = {A recursion-theoretic analysis of the clopen {R}amsey {T}heorem},
	Volume = {49},
	Year = {1984}}

@book{Cohen:66,
	Author = {Cohen, Paul J.},
	Publisher = {W. A. Benjamin},
	Title = {Set Theory and the Continuum Hypothesis},
	Year = {1966}}

@inproceedings{Cook:71,
	Author = {Cook, S. A.},
	Booktitle = {Proc. Third Annual ACM Sympos. on Theory of Compt.},
	Pages = {151--158},
	Title = {The Complexity of Theorem Proving Procedures},
	Year = {1971}}

@article{Cooper.Copestake:88,
	Author = {Cooper, S. Barry and Copestake, C. S.},
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	Title = {Properly ${\Sigma}_2$ enumeration degrees},
	Volume = {34},
	Year = {1988}}

@article{Cooper.Harrington.ea:91,
	Author = {Cooper, S. Barry and Harrington, Leo A. and Lachlan, Alistair H. and Lempp, Steffen and Soare, Robert I.},
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	Pages = {125--151},
	Title = {The d.r.e. degrees are not dense},
	Volume = {55},
	Year = {1991}}

@article{Cooper.Lempp.ea:89,
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	Journal = {Israel J. Math.},
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	Title = {Weak density and cupping in the d-r.e. degrees},
	Volume = {67},
	Year = {1989}}

@article{Cooper.McEnvoy:85,
	Author = {S. Barry Cooper and K. McEnvoy},
	Journal = {J. Symbolic Logic},
	Pages = {839--848},
	Title = {On Minimal Pairs of Enumeration Degrees},
	Volume = {50},
	Year = {1985}}

@unpublished{Cooper.Sorbi:95,
	Author = {S. Barry Cooper and Andrea Sorbi},
	Note = {Preprint},
	Title = {Noncappable Enumeration Degrees Below $\mathbf{0}'_e$},
	Year = {1995}}

@unpublished{Cooper.Sui.ea:94,
	Author = {Cooper, S. Barry and Sui, Y. and Yi, X.},
	Note = {Unpublished},
	Title = {Minimal pairs and the {Slaman--Soare} phenomenon},
	Year = {1994}}

@unpublished{Cooper.Yi:nd,
	Author = {Cooper, Barry and Yi, Xiaoding},
	Note = {In preparation},
	Title = {Non-splitting and the high/low hierarchy}}

@phdthesis{Cooper:71,
	Author = {S. Barry Cooper},
	School = {Leicester University},
	Title = {Degrees of Unsolvability},
	Year = {1971}}

@article{Cooper:73,
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	Journal = {J. Symbolic Logic},
	Pages = {249-271},
	Title = {Minimal degrees and the jump operator},
	Volume = {38},
	Year = {1973}}

@article{Cooper:74,
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	Journal = {J. Symbolic Logic},
	Pages = {655--660},
	Title = {Minimal Pairs and High Recursively Enumerable Degrees},
	Volume = {39},
	Year = {1974}}

@unpublished{Cooper:74*1,
	Author = {S. Barry Cooper},
	Note = {Handwritten notes},
	Title = {On a Theorem of C.~E.~M.~Yates},
	Year = {1974}}

@article{Cooper:82,
	Author = {Cooper, S. B.},
	Journal = {J. Symbolic Logic},
	Pages = {854--859},
	Title = {Partial degrees and the density problem},
	Volume = {47},
	Year = {1982}}

@article{Cooper:87,
	Author = {S. Barry Cooper},
	Journal = {Z. Math. Logik Grundlag. Math.},
	Pages = {537--560},
	Title = {Enumeration reducibility using bounded information: counting minimal covers},
	Volume = {33},
	Year = {1987}}

@article{Cooper:89,
	Author = {S. Barry Cooper},
	Journal = {J. Symbolic Logic},
	Pages = {324--353},
	Title = {A Jump Class of Noncappable Degrees},
	Volume = {54},
	Year = {1989}}

@article{Cooper:90,
	Author = {Cooper, S. B.},
	Journal = {Bull. Amer. Math. Soc.},
	Pages = {151-158},
	Title = {The jump is definable in the structure of the degrees of unsolvability},
	Volume = {23},
	Year = {1990}}

@inproceedings{Cooper:90*1,
	Address = {Heidelberg},
	Author = {Cooper, S. B.},
	Booktitle = {Recursion Theory Week, Oberwolfach 1989},
	Editor = {K. Ambos-Spies and G. M{\"u}ller and Gerald E. Sacks},
	Pages = {57--110},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Enumeration reducibility, nondeterministic computations and relative computability of partial functions},
	Volume = {1432},
	Year = {1990}}

@inproceedings{Cooper:91,
	Author = {Cooper, S. B.},
	Booktitle = {Logic Colloquium '90},
	Editor = {J. Oikkonen and J. V\"a\"an\"anen},
	Pages = {25--45},
	Series = {Lecture Notes in Logic},
	Title = {Definability and Global Degree Theory},
	Volume = {2},
	Year = {1991}}

@article{Cooper:92,
	Author = {S. Barry Cooper},
	Journal = {Proc. Amer. Math. Soc.},
	Pages = {461--472},
	Title = {A Splitting Theorem for the $n$-Recursively Enumerable Degrees},
	Volume = {115},
	Year = {1992}}

@proceedings{Cooper:94,
	Author = {Cooper, S. B.},
	Editors = {Prawitz, D. and Westerst\aahl, D},
	Publisher = {Kluwer Academic Publishers},
	Series = {Proceedings of the International Congress for Logic, Methodology and the Philosophy of Science (Uppsala, 1991)},
	Title = {Rigidity and definability in the noncomputable universe},
	Year = {1994}}

@incollection{Cooper:96,
	Address = {Berlin},
	Author = {Cooper, S. Barry},
	Booktitle = {Algebra and analysis (Kazan, 1994)},
	Mrclass = {03D25 (03D30 03D35)},
	Mrnumber = {98i:03056},
	Mrrevr = {Peter Cholak},
	Pages = {41--55},
	Publisher = {de Gruyter},
	Title = {Discontinuous phenomena and {T}uring definability},
	Year = {1996}}

@incollection{Cooper:99,
	Author = {S.B. Cooper},
	Booktitle = {Handbook of computability theory},
	Chapter = {4},
	Editor = {Edward R. Griffor},
	Pages = {121--154},
	Publisher = {North--Holland Publishing Co.},
	Series = {Studies in Logic},
	Title = {Local degree theory},
	Volume = {140},
	Year = {1999}}

@unpublished{Cooper:nd,
	Author = {S. Barry Cooper},
	Note = {To appear},
	Title = {The Density of the Low$_2$ $n$-Recursively Enumerable Degrees}}

@book{Crossley.Remmel.ea:93,
	Address = {Boston Mass.},
	Editor = {J.N.C. Crossley and J. Remmel and Shore, R.A. and M. Sweedler},
	Publisher = {Birk\" auser},
	Title = {Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday},
	Year = {1993}}

@article{Daley:86,
	Author = {R. P. Daley},
	Journal = {Lecture Notes in Computer Science},
	Pages = {73--82},
	Title = {Inductive Inference Hierarchies: Probabilistic vs Pluralistic},
	Volume = {215},
	Year = {1986}}

@article{Davis.Putnam.ea:61,
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	Journal = {Ann. of Math. (2)},
	Pages = {425--436},
	Title = {The decision problem for exponential {D}iophantine equations},
	Volume = {74},
	Year = {1961}}

@book{Davis:65,
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	Publisher = {Raven Press, Hewlett, N.Y.},
	Title = {The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions},
	Year = {1965}}

@article{Dawar.Lindell.ea:nd,
	Author = {Anuj Dawar and Steven Lindell and Scott Weinstein},
	Journal = {Inform. and Control},
	Title = {Infinitary Logic and Inductive Definability over Finite Structures}}

@incollection{Degtev:81,
	Author = {A. Degtev},
	Booktitle = {Algebraic Systems},
	Editor = {D. I. Moldavanskii},
	Note = {(in Russian)},
	Pages = {88--99},
	Publisher = {Wadsworth International},
	Title = {$(m,n)$-computable sets},
	Year = {1981}}

@article{Dehn:12,
	Author = {Dehn, M.},
	Journal = {Math. Ann.},
	Pages = {116-144},
	Title = {\"{U}ber unendliche diskontinuierliche Gruppen},
	Volume = {71},
	Year = {1912}}

@article{Dekker.Myhill:58,
	Author = {Dekker, J. and Myhill, J.},
	Journal = {Canad. J. Math.},
	Pages = {357--373},
	Title = {Retraceable sets},
	Volume = {10},
	Year = {1958}}

@article{Dekker:54,
	Author = {J. C. E. Dekker},
	Journal = {Proc. Amer. Math. Soc.},
	Pages = {791--796},
	Title = {A Theorem on Hypersimple Sets},
	Volume = {5},
	Year = {1954}}

@article{Dekker:81,
	Author = {J. C. E. Dekker},
	Journal = {J. Symbolic Logic},
	Pages = {539--571},
	Title = {Twilight Graphs},
	Volume = {46},
	Year = {1981}}

@article{Denisov:72,
	Author = {S. D. Denisov},
	Journal = {Algebra and Logic},
	Pages = {418--443},
	Title = {The structure of the uppersemilattice of recursively enumerable $m$-degrees and related questions, {I}},
	Volume = {17},
	Year = {1972}}

@book{Diestel:97,
	Address = {New York},
	Author = {Diestel, Reinhard},
	Isbn = {0-387-98210-8},
	Mrclass = {05-01},
	Mrnumber = {1 448 665},
	Note = {Translated from the 1996 German original},
	Pages = {xiv+289},
	Publisher = {Springer-Verlag},
	Title = {Graph theory},
	Year = {1997}}

@unpublished{Downey.Fellows:nd,
	Author = {R. G. Downey and M. Fellows},
	Note = {In preparation},
	Title = {Fixed Parameter Tractability and Intractability: A Survey}}

@article{Downey.Harrington:96,
	Author = {Downey, Rod and Harrington, Leo},
	Coden = {APALD7},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Number = {3},
	Pages = {277--289},
	Title = {There is no fat orbit},
	Volume = {80},
	Year = {1996}}

@inproceedings{Downey.Jockusch.ea:90,
	Address = {Heidelberg},
	Author = {R. G. Downey and Jockusch, Jr., Carl G. and M. Stob},
	Booktitle = {Recursion Theory Week, Oberwolfach 1989},
	Editor = {K. Ambos-Spies and G. H. Muller and Gerald E. Sacks},
	Pages = {141--174},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Array Nonrecursive Sets and Multiple Permitting Arguments},
	Volume = {1432},
	Year = {1990}}

@article{Downey.Jockusch:87,
	Author = {R. G. Downey and Jockusch, Jr., Carl G.},
	Journal = {Trans. Amer. Math. Soc.},
	Pages = {103--137},
	Title = {{$\mathbf{T}$}-degrees, Jump Classes, and Strong Reducibilities},
	Volume = {30},
	Year = {1987}}

@article{Downey.Knight:92,
	Author = {Downey, R. G. and Knight, J.},
	Journal = {Proc. Amer. Math. Soc.},
	Pages = {545-552},
	Title = {Orderings with $\alpha$th jump degree $\mathbf{0}^{(\alpha)}$},
	Volume = {114},
	Year = {1992}}

@unpublished{Downey.Lempp.ea:nd,
	Author = {Rodney G. Downey and Steffen Lempp and Richard A. Shore},
	Note = {To appear},
	Title = {Highness and Bounding Minimal Pairs}}

@article{Downey.Lempp:97,
	Author = {Downey, Rodney G. and Lempp, Steffen},
	Coden = {JSYLA6},
	Fjournal = {The Journal of Symbolic Logic},
	Issn = {0022-4812},
	Journal = {J. Symbolic Logic},
	Number = {4},
	Pages = {1215--1240},
	Title = {Contiguity and distributivity in the enumerable {T}uring degrees},
	Volume = {62},
	Year = {1997}}

@article{Downey.Lempp:nd,
	Author = {R. G. Downey and Steffen Lempp},
	Journal = {J. Symbolic Logic},
	Note = {To appear},
	Title = {Contiguity and Distributivity in the Computably Enumerable Turing Degrees}}

@article{Downey.Moses:89,
	Author = {Rodney Downey and Michael Moses},
	Journal = {Z. Math. Logik Grundlag. Math.},
	Pages = {237--246},
	Title = {On choice sets and strongly non-trivial self-embeddings of recursive linear orders},
	Volume = {35},
	Year = {1989}}

@article{Downey.Remmel.ea:87,
	Author = {R. G. Downey and J. B. Remmel and L. V. Welch},
	Journal = {Trans. Amer. Math. Soc.},
	Pages = {683--714},
	Title = {Degrees of Splittings and Bases of Recursively Enumerable Subspaces},
	Volume = {302},
	Year = {1987}}

@article{Downey.Remmel:89,
	Author = {R. G. Downey and J. B. Remmel},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {105--125},
	Title = {Classification of Degree Classes Associated with Recursively Enumerable Subspaces},
	Volume = {42},
	Year = {1989}}

@article{Downey.Shore:95,
	Author = {R. G. Downey and Richard A. Shore},
	Journal = {J. Symbolic Logic},
	Number = {3},
	Pages = {727--756},
	Title = {Degree Theoretic Definitions of Low$_2$ Recursively Enumerable Sets},
	Volume = {60},
	Year = {1995}}

@article{Downey.Shore:96,
	Author = {R. G. Downey and Richard A. Shore},
	Journal = {Israel J. Math.},
	Pages = {221-246},
	Title = {Lattice Embedding below a NonLow$_2$ Recursively Enumerable Degree},
	Volume = {94},
	Year = {1996}}

@unpublished{Downey.Shore:nd,
	Author = {R. G. Downey and Richard A. Shore},
	Note = {To appear},
	Title = {Decomposition and Infima in the Recursively Enumerable Degrees}}

@unpublished{Downey.Shore:nd*2,
	Author = {Downey, R. and Shore, R. A.},
	Journal = {Israel J. Math.},
	Note = {to appear},
	Title = {Lattice embeddings below a nonlow$_2$ recursively enumerable degree}}

@article{Downey.Slaman:89,
	Author = {Downey, R. G. and Slaman, Theodore A.},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {119--152},
	Title = {Completely mitotic r. e. degrees},
	Volume = {41},
	Year = {1989}}

@article{Downey.Slaman:92,
	Author = {Downey, R. G. and Slaman, Theodore A.},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {221--237},
	Title = {On co-simple isols and their intersection types},
	Volume = {56},
	Year = {1992}}

@article{Downey.Stob:86,
	Author = {R. G. Downey and M. Stob},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {205--236},
	Title = {Structural Interactions of the {$\mathbf{T}$}- and W-Degrees},
	Volume = {31},
	Year = {1986}}

@inproceedings{Downey.Stob:90,
	Author = {R. G. Downey and M. Stob},
	Booktitle = {Proceedings of the Fourth Asian Logic Conference},
	Pages = {75--87},
	Publisher = {CSSK Centre},
	Title = {Automorphisms and Splittings of Recursively Enumerable Sets},
	Year = {1990}}

@article{Downey.Stob:91,
	Author = {R. G. Downey and M. Stob},
	Journal = {Z. Math. Logik Grundlag. Math.},
	Pages = {113--120},
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	Volume = {37},
	Year = {1991}}

@article{Downey.Stob:92,
	Author = {R. G. Downey and M. Stob},
	Journal = {Adv. in Math.},
	Pages = {237--265},
	Title = {Automorphisms of the Lattice of Recursively Enumerable Sets: Orbits},
	Volume = {92},
	Year = {1992}}

@article{Downey.Stob:93,
	Author = {Downey, Rod and Stob, Michael},
	Coden = {APALD7},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03D25},
	Mrnumber = {95c:03099},
	Mrrevr = {E. Herrmann},
	Number = {1},
	Pages = {106 pp},
	Title = {Splitting theorems in recursion theory},
	Volume = {65},
	Year = {1993}}

@article{Downey.Stob:93*1,
	Author = {Downey, Rod and Stob, Michael},
	Coden = {APALD7},
	Fjournal = {Annals of Pure and Applied Logic},
	Issn = {0168-0072},
	Journal = {Ann. Pure Appl. Logic},
	Mrclass = {03D25},
	Mrnumber = {94d:03082},
	Mrreviewer = {Xi Zhong Zheng},
	Note = {Fourth Asian Logic Conference (Tokyo, 1990)},
	Number = {3},
	Pages = {175--199},
	Title = {Friedberg splittings of recursively enumerable sets},
	Volume = {59},
	Year = {1993}}

@unpublished{Downey.Stob:nd,
	Author = {R. G. Downey and M. Stob},
	Note = {To appear},
	Title = {Minimal Pairs in Lower Cones}}

@article{Downey.Welch:86,
	Author = {R. G. Downey and L. V. Welch},
	Journal = {J. Symbolic Logic},
	Pages = {88--109},
	Title = {Splitting Properties of Recursively Enumerable Sets and Degrees},
	Volume = {51},
	Year = {1986}}

@article{Downey:85,
	Author = {R. G. Downey},
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	Pages = {337--351},
	Title = {The Degrees of R. E. Sets Without the Universal Splitting Property},
	Volume = {291},
	Year = {1985}}

@article{Downey:87,
	Author = {R. G. Downey},
	Journal = {Pacific J. Math.},
	Pages = {299--319},
	Title = {Subsets of Hypersimple Sets},
	Volume = {127},
	Year = {1987}}

@article{Downey:87*1,
	Author = {R. G. Downey},
	Journal = {Illinois J. Math.},
	Pages = {419--427},
	Title = {{$\Delta^0_2$} Degrees and Transfer Theorems},
	Volume = {31},
	Year = {1987}}

@article{Downey:87*2,
	Author = {Downey, R. G.},
	Coden = {AMLGAN},
	Fjournal = {Archiv f\"ur Mathematische Logik und Grundlagenforschung},
	Issn = {0003-9268},
	Journal = {Arch. Math. Logik Grundlag.},
	Mrclass = {03D25 (03D30)},
	Mrnumber = {88h:03058},
	Mrrevr = {C. G. Jockusch, Jr.},
	Number = {3-4},
	Pages = {127--136},
	Title = {Localization of a theorem of {A}mbos-{S}pies and the strong antisplitting property},
	Volume = {26},
	Year = {1987}}

@article{Downey:89,
	Author = {R. G. Downey},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {1--27},
	Title = {Intervals and Sublattices of the Recursively Enumerable {$\mathbf{T}$}- and W-Degrees, Part {I}: Density},
	Volume = {49},
	Year = {1989}}

@article{Downey:89*1,
	Author = {R. G. Downey},
	Journal = {Bull. London Math. Soc.},
	Pages = {43--50},
	Title = {$D$-Recursively Enumerable Degrees and the Nondiamond Theorem},
	Volume = {21},
	Year = {1989}}

@article{Downey:90,
	Author = {R. G. Downey},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {97--119},
	Title = {Lattice Nonembedding and Intial Segments of the R. E. Degrees},
	Volume = {49},
	Year = {1990}}

@inproceedings{Downey:90*1,
	Address = {Heidelberg},
	Author = {R. G. Downey},
	Booktitle = {Recursion Theory Week, Oberwolfach 1989},
	Editor = {K. Ambos-Spies and G. H. Muller and Gerald E. Sacks},
	Pages = {1--22},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Notes on the $\mathbf{0}'''$ Priority Method with Special Attention to Density Results},
	Volume = {1432},
	Year = {1990}}

@article{Downey:93,
	Author = {R. G. Downey},
	Journal = {Illinois J. Math.},
	Note = {To appear},
	Title = {Array Nonrecursive Degrees and Lattice Embeddings of the Diamond},
	Year = {1993}}

@incollection{Downey:nd,
	Author = {Rodney Downey},
	Booktitle = {Handbook of Recursive Algebra},
	Editor = {Ershov and Goncharov and Nerode and Remmel},
	Publisher = {North--Holland Publishing Co.},
	Title = {Recursion Theory and Linear Orderings}}

@book{Ebbinghaus.Flum:95,
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	Year = {1995}}

@proceedings{Ebbinghaus.Muller.ea:85,
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	Note = {418 pp.},
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	Series = {Lecture Notes in Mathematics},
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	Volume = {1141},
	Year = {1985}}

@article{Ehrenfeucht:69,
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	Journal = {Fund. Math.},
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@article{Elgot.Rabin:66,
	Author = {Calvin C. Elgot and Michael O. Rabin},
	Journal = {J. Symbolic Logic},
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	Volume = {31},
	Year = {1966}}

@article{Elgot:61,
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	Title = {Decision problems of finite automata design and related arithmetics},
	Volume = {{98}},
	Year = {1961}}

@article{Ellentuck:74,
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	Pages = {163--165},
	Title = {A new proof that analytic sets are {R}amsey},
	Volume = {39},
	Year = {1974}}

@inproceedings{Epstein.Haas.ea:81,
	Address = {Heidelberg},
	Author = {Richard L. Epstein and Richard Haas and Richard L. Kramer},
	Booktitle = {Logic Year 1979--80},
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	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {Hierarchies of Sets and Degrees Below {${\bf 0}'$}},
	Volume = {859},
	Year = {1981}}

@article{Epstein:75,
	Author = {Epstein, R. L.},
	Journal = {Mem. Amer. Math. Soc.},
	Title = {Minimal degrees of unsolvability and the full approximation construction},
	Volume = {162},
	Year = {1975}}

@book{Epstein:79,
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	Series = {Lecture Notes in Mathematics},
	Title = {Degrees of Unsolvability: Structure and Theory},
	Volume = {759},
	Year = {1979}}

@article{Ershov.Lavrov.ea:65,
	Author = {Ershov and Lavrov and Taimonv and Taitslin},
	Journal = {Russian Math. Surveys},
	Title = {The undecidability of certain theories},
	Volume = {20},
	Year = {1965}}

@article{Ershov.Lavrov.ea:65*1,
	Author = {Y. Ershov and I. Lavrov and A. Taimanov and M. Taitslin},
	Journal = {Russian Math Surveys},
	Pages = {35--105},
	Title = {Elementary theories},
	Volume = {20},
	Year = {1965}}

@article{Ershov.Taitslin:63,
	Author = {Yu. Ershov and M. Taitslin},
	Journal = {Algebra i Logika},
	Pages = {37--41},
	Title = {The undecidability of certain theories},
	Volume = {2},
	Year = {1963}}

@article{Ershov:68,
	Author = {Yu. L. Ershov},
	Journal = {Algebra i Logika},
	Month = {January--February},
	Note = {English Translation, Consultants Bureau, NY, pp.~25--43},
	Number = {1},
	Pages = {47--74},
	Title = {A Hierarchy of Sets, {I}},
	Volume = {7},
	Year = {1968}}

@article{Ershov:68*1,
	Author = {Yu. L. Ershov},
	Journal = {Algebra i Logika},
	Month = {July--August},
	Note = {English Translation, Consultants Bureau, NY, pp.~212--232},
	Number = {4},
	Pages = {15--47},
	Title = {A Hierarchy of Sets, {II}},
	Volume = {7},
	Year = {1968}}

@article{Ershov:70,
	Author = {Yu. L. Ershov},
	Journal = {Algebra i Logika},
	Month = {January--February},
	Note = {English Translation, Consultants Bureau, NY, pp.~20--31},
	Number = {1},
	Pages = {34--51},
	Title = {A Hierarchy of Sets, {III}},
	Volume = {9},
	Year = {1970}}

@article{Ershov:75,
	Author = {Ershov, Yu. L.},
	Journal = {Algebra i Logika},
	Note = {Russian},
	Pages = {258-284, 368},
	Title = {The upper semilattice of numerations of a finite set},
	Volume = {14},
	Year = {1975}}

@book{Fagin.Halpern.ea:95,
	Address = {Cambridge},
	Author = {R. Fagin and J. Y. Halpern and Y. Moses and M. Y. Vardi},
	Descriptor = {Wissensbasierter Entwurf, Wissensbasiert, Knowledge-based, Knowledge-Base, Knowledge},
	Isbn = {0-262-06162-7},
	Publisher = {MIT-Press},
	Title = {Reasoning About Knowledge},
	Year = {1995}}

@article{Feferman.Vaught:59,
	Author = {Feferman and Vaught},
	Journal = {Fund. Math.},
	Pages = {57--103},
	Title = {The first-order properties of algebraic systems},
	Volume = {47},
	Year = {1959}}

@inproceedings{Feferman:65,
	Address = {Amsterdam},
	Author = {Feferman, S.},
	Booktitle = {The Theory of Models, Proceedings of the 1963 International Symposium at Berkeley},
	Editor = {J. W. Addison and L. Henkin and A. Tarski},
	Pages = {89--95},
	Publisher = {North--Holland Publishing Co.},
	Series = {Studies in Logic and the Foundations of Mathematics},
	Title = {Some applications of the notions of forcing and generic sets},
	Year = {1965}}

@article{Feiner:74,
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	Journal = {J. Symbolic Logic},
	Pages = {365-74},
	Title = {Hierarchies of Boolean algebras},
	Volume = {35},
	Year = {1974}}

@inproceedings{Fejer.Shore:85,
	Address = {Heidelberg},
	Author = {Fejer, P. A. and Shore, Richard A.},
	Booktitle = {Recursion Theory Week},
	Editor = {H.-D. Ebbinghaus and G. H. Muller and Gerald E. Sacks},
	Pages = {121--140},
	Publisher = {Springer--Verlag},
	Title = {Embeddings and extensions of embeddings in the r. e. tt- and wtt-degrees},
	Year = {1985}}

@inproceedings{Fejer.Soare:81,
	Author = {P. A. Fejer and Robert I. Soare},
	Booktitle = {Logic Year 1979--80: University of {C}onnecticut},
	Pages = {49--62},
	Title = {The Plus-Cupping Theorem for the Recursively Enumerable Degrees},
	Year = {1981}}

@article{Fejer:82,
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	Journal = {Trans. Amer. Math. Soc.},
	Pages = {157--180},
	Title = {Branching Degrees Above Low Degrees},
	Volume = {273},
	Year = {1982}}

@article{Fejer:83,
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	Pages = {113--130},
	Title = {The Density of the Nonbranching Degrees},
	Volume = {24},
	Year = {1983}}

@article{Fejer:89,
	Author = {Fejer, P. A.},
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	Volume = {35},
	Year = {1989}}

@proceedings{Fenstad.Gandy.ea:78,
	Address = {Amsterdam},
	Editor = {Jens Erik Fenstad and R. O. Gandy and Gerald E. Sacks},
	Title = {Generalized Recursion Theory {II}},
	Year = {1978}}

@proceedings{Fenstad.Gandy.ea:78*1,
	Address = {Amsterdam},
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	Note = {417 pp.},
	Publisher = {North--Holland Publishing Co.},
	Title = {Generalized Recursion Theory},
	Year = {1978}}

@article{Fortnow.Gasarch.ea:94,
	Annote = {Subsumes the COLT paper by Gasarch and Pleszkoch entitled{\newline}		  {\it Learning via Queries to an Oracle}},
	Author = {L. Fortnow and W. Gasarch and S. Jain and E. Kinber and M. Kummer and S. Kurtz and M. Pleszkoch and T. Slaman and R. Solovay and F. Stephan},
	Journal = {Ann. Pure Appl. Logic},
	Pages = {21--276},
	Title = {Extremes in the Degrees of Inferability},
	Volume = {66},
	Year = {1994}}

@article{Friedberg.Rogers:59,
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	Journal = {Z. Math. Logik Grundlag. Math.},
	Pages = {117--125},
	Title = {Reducibility and Completeness for Sets of Integers},
	Volume = {5},
	Year = {1959}}

@article{Friedberg:57,
	Author = {Friedberg, R. M.},
	Journal = {J. Symbolic Logic},
	Pages = {159--160},
	Title = {A criterion for completeness of degrees of unsolvability},
	Volume = {22},
	Year = {1957}}

@article{Friedberg:57*1,
	Author = {Friedberg, R. M.},
	Journal = {Proc. Nat. Acad. Sci. U.S.A.},
	Pages = {236--238},
	Title = {Two recursively enumerable sets of incomparable degrees of unsolvability (solution to Post's problem, 1944)},
	Volume = {43},
	Year = {1957}}

@article{Friedberg:58,
	Author = {Friedberg, R. M.},
	Journal = {J. Symbolic Logic},
	Pages = {309--316},
	Title = {Three theorems on recursive enumeration. {I}. Decomposition. {II.} Maximal set. {III.} Enumeration without duplication.},
	Volume = {23},
	Year = {1958}}

@inproceedings{Friedberg:60,
	Author = {Friedberg, R. M.},
	Booktitle = {Summaries of talks presented at the summer institute for symbolic logic, 1957, Cornell University},
	Note = {second edition},
	Organization = {{I}nstitute for {D}efence {A}nalyses},
	Pages = {404--406},
	Title = {The fine structure of the degrees of unsolvability of recursively enumerable sets},
	Year = {1960}}

@inproceedings{Friedman.Robertson.ea:87,
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	Publisher = {American Mathematical Society},
	Series = {Contemporary Mathematics},
	Title = {The metamathatics of the Graph Minor Theorem},
	Volume = {65},
	Year = {1987}}

@article{Friedman.Sacks:77,
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	Journal = {Bull. Amer. Math. Soc.},
	Pages = {255--256},
	Title = {Inadmissible Recursion Theory},
	Volume = {83},
	Year = {1977}}

@incollection{Friedman.Simpson:00,
	Address = {Providence, RI},
	Author = {Friedman, Harvey and Simpson, Stephen G.},
	Booktitle = {Computability theory and its applications (Boulder, CO, 1999)},
	Mrclass = {03F35 (03B30 05D10 26E40 46Bxx)},
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	Pages = {127--144},
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	Year = {2000}}

@article{Friedman:75,
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	Pages = {235--242},
	Publisher = {Canad. Math. Congress, Montreal, Que.},
	Title = {Some systems of second order arithmetic and their use},
	Year = {1975}}

@article{Friedman:75*1,
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	Journal = {J. Symbolic Logic},
	Pages = {113--129},
	Title = {102 Problems in Mathematical Logic},
	Volume = {40},
	Year = {1975}}

@article{Friedman:76,
	Author = {Harvey Friedman},
	Journal = {Journal of Symbolic Logic},
	Pages = {557--559},
	Title = {Systems of second order arithmetic with restricted induction, {I}, {II} {$($}abstracts{$)$}},
	Volume = {41},
	Year = {1976}}

@article{Froehlich.Shepherdson:55,
	Author = {A. Froehlich and J. C. Shepherdson},
	Journal = {Phil. Transactions of the Royal Society of London (Series A)},
	Pages = {407--432},
	Title = {Effective Procedures in Field Theory},
	Volume = {248},
	Year = {1955}}

@article{Gaifman:64,
	Author = {Haim Gaifman},
	Journal = {Notices Amer. Math. Soc.},
	Pages = {771},
	Title = {Measureable cardinals and constructible sets},
	Volume = {11},
	Year = {1964}}

@article{Galvin.Prikry:73,
	Author = {F. Galvin and K. Prikry},
	Journal = {J. Symbolic Logic},
	Pages = {193--198},
	Title = {{B}orel Sets and {R}amsey's Theorem},
	Volume = {38},
	Year = {1973}}

@article{Gandy.Sacks:67,
	Author = {Robin O. Gandy and Gerald E. Sacks},
	Journal = {Fund. Math.},
	Pages = {215--223},
	Title = {A Minimal Hyperdegree},
	Volume = {61},
	Year = {1967}}

@book{Garey.Johnson:79,
	Address = {New York},
	Author = {Michael R. Garey and David S. Johnson},
	Publisher = {W. H. Freeman and Company},
	Title = {Computers and Intractability},
	Year = {1979}}

@inproceedings{Gasarch.Guimaraes:92,
	Address = {Heidelberg},
	Author = {William Gasarch and Katia Guimaraes},
	Booktitle = {First Latin American Sym. on Theoretical Informatics (LATIN 92)},
	Pages = {177--190},
	Publisher = {Springer--Verlag},
	Series = {Lecture notes in Computer Science},
	Title = {On the number of components of a recursive graph},
	Volume = {583},
	Year = {1992}}

@article{Gasarch.Kueker.ea:89,
	Author = {William Ian Gasarch and Dave Kueker and Dave Mount},
	Journal = {Congressus Numerantium},
	Pages = {97--102},
	Title = {Recursive Categoricity of Highly Recursive Graphs},
	Year = {1989}}

@article{Gasarch.Pleszkoch.ea:92,
	Annote = {Earlier version in COLT90},
	Author = {W. Gasarch and M. Pleszkoch and R. Solovay},
	Journal = {J. Symbolic Logic},
	Number = {1},
	Pages = {53--81},
	Title = {Learning via Queries to $[+,<]$},
	Volume = {57},
	Year = {1992}}

@article{Gasarch.Smith:92,
	Author = {W. Gasarch and C. H. Smith},
	Journal = {J. Assoc. Comput. Mach.},
	Note = {A shorter version is in 29th FOCS conference, 1988, pp. 130-137},
	Number = {3},
	Pages = {649--675},
	Title = {Learning via Queries},
	Volume = {39},
	Year = {1992}}

@incollection{Gasarch:nd,
	Author = {William I. Gasarch},
	Booktitle = {Handbook of Recursive Algebra},
	Editor = {Ershov and Goncharov and Nerode and Remmel},
	Publisher = {North--Holland Publishing Co.},
	Title = {A Survey of Recursive Combinatorics}}

@article{Godel:31,
	Author = {G{\"o}del, Kurt},
	Journal = {Monatsh. Math. Phys.},
	Pages = {349--360},
	Title = {{\"U}ber formal unentscheidbare S{\"a}tze der Principia Mathematica und verwandter Systeme {I}},
	Volume = {38},
	Year = {1931}}

@article{Godel:38,
	Author = {Kurt G{\"o}del},
	Journal = {Proc. Nat. Acad. Sci. U.S.A.},
	Pages = {556--557},
	Title = {The consistency of the axiom of choice and of the generalized continuum hypothesis},
	Volume = {24},
	Year = {1938}}

@inproceedings{Godel:65,
	Address = {New York},
	Author = {G{\"o}del, Kurt},
	Booktitle = {The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions},
	Editor = {Martin Davis},
	Pages = {39--71},
	Publisher = {Raven Press, Hewlitt},
	Title = {On undecidable propositions of formal mathematical systems},
	Year = {1965}}

@incollection{Godel:86,
	Address = {Oxford},
	Author = {G{\"o}del, Kurt},
	Booktitle = {Kurt G{\"o}del: Collected Works},
	Editor = {Feferman, Solomon and Dawson, Jr., John W. and Kleene, Stephen C. and Moore, Gregory H. and Solovay, Robert M. and {Van Heijenoort}, Jean},
	Pages = {235--237},
	Publisher = {Oxford University Press},
	Title = {On completeness and consistency},
	Volume = {1},
	Year = {1986}}

@article{Gold:65,
	Author = {E. Mark Gold},
	Journal = {J. Symbolic Logic},
	Number = {1},
	Pages = {28--48},
	Title = {Limiting Recursion},
	Volume = {30},
	Year = {1965}}

@book{Graham.Rothschild.ea:80,
	Address = {New York},
	Author = {Graham, Ronald L. and Rothschild, Bruce L. and Spencer, Joel H.},
	Note = {A Wiley-Interscience Publication},
	Publisher = {John Wiley \& Sons, Inc.},
	Series = {Wiley-Interscience Series in Discrete Mathematics},
	Title = {Ramsey theory},
	Year = {1980}}

@book{Gratzer:71,
	Address = {San Francisco},
	Author = {Gr\"{a}tzer, G.},
	Publisher = {W.H. Freeman},
	Series = {A series of Books in Mathematices},
	Title = {Lattice Theory: First Concepts and Distributive Lattices},
	Year = {1971}}

@article{Groszek.Mytilinaios.ea:nd,
	Author = {Groszek, Marcia J. and Mytilinaios, M. E. and Slaman, Theodore A.},
	Journal = {J. Symbolic Logic},
	Note = {To appear},
	Title = {The {S}acks density theorem and ${\Sigma}_2$-bounding}}

@inproceedings{Groszek.Mytilinaios:90,
	Address = {Heidelberg},
	Author = {Groszek, Marcia J. and Mytilinaios, M. E.},
	Booktitle = {Recursion Theory Week, Oberwolfach 1989},
	Editor = {K. Ambos-Spies and G. H. Muller and Gerald E. Sacks},
	Pages = {205--223},
	Publisher = {Springer--Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {${\Sigma}_2$-Induction and the construction of a high degree},
	Volume = {1432},
	Year = {1990}}

@article{Groszek.Slaman:83,
	Author = {Groszek, Marcia J. and Slaman, Theodore A.},
	Journal = {Trans. Amer. Math. Soc.},
	Pages = {579--587},
	Title = {Independence results on the global structure of the {T}uring degrees},
	Volume = {277},
	Year = {1983}}

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@unpublished{Herrmann.Kummer:nd,
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@unpublished{Herrmann:nd,
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@book{Hopcroft.Ullman:79,
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	Year = {1979}}

@unpublished{Hummel.Jockusch:nd,
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	Note = {To Appear in J. Symbolic Logic},
	Title = {Generalized Cohesiveness}}

@article{Hummel:94,
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	Journal = {J. Symbolic Logic},
	Pages = {1301--1325},
	Title = {Effective Versions of {R}amsey's Theorem: Avoiding the Cone Above $\mbox{\bfseries{0}}'$},
	Volume = {59},
	Year = {1994}}

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	Volume = {36},
	Year = {1990}}

@phdthesis{Ingrassia:81,
	Author = {M. Ingrassia},
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