Research Interests

I study problems in computable model theory and reverse mathematics. The aim of computable model theory is to study the complexity of structures from a computable or algorithmic perspective. Reverse mathematics deems two mathematical statements to have the same proof theoretic strength if each statement can be used to prove the other over some weak base system of axioms. If two statements are equivalent in reverse mathematics, they depend on the exact same underlying principles. Computable model theory and reverse mathematics calibrate the complexity of mathematical problems in complementary but distinct ways, and together they illuminate common processes throughout mathematics. My research has focused on the computability and reverse mathematics of homogeneous models, an important object in classical model theory.

Selected Publications

• "The degree spectra of homogeneous models," K. Lange, to appear in the Journal of Symbolic Logic.
• "A characterization of the O-basis homogeneous bounding degrees," K. Lange, in preparation.
• "Computability of homogeneous models," K. Lange, R. Soare, Notre Dame Journal of Formal Logic, Vol. 48 (2007) Pages 143-170.
• "Pattern, linesums, and symmetry," E.E. Eischen, C.R. Johnson, K. Lange, D. Stanford Linear Algebra and its Applications (LAA)< Vol. 357 (2002) Pages 273-289.