Non-research Papers and Talks

Notes for a talk I gave on a proof showing the theory of (Z,+) does not have a prime model, but does have a lot of distinct minimal models. This shows that the different ways of defining a "smallest" or "simplest" model are not equivalent. The abstract is:

The vagueness of the phrase ``simplest possible'' is shown through the sometimes coinciding sometimes wildly diverging notions of "prime model", a model which can be embedded inside any other model of a given theory, and a "minimal model", a model which does not contain any submodels of a given theory. Hijinks ensue. The highlight will be the exhibition of a theory with no prime model and uncluntably many minimal models along with a proof of this fact due to Baldwin, Blass, Glass, and Kueker.

These are notes I made and papers I found on prime testing algorithms. The focus is more on complexity issues than implementation details.