Sergey Sudoplatov : Through Lachlan Problem and Generic Constructions to Classification of Countable Models of Complete Theories

Posted by Isaac Goldbring , part of the Logic Seminar.

At

March 12, 2013, 4 p.m.

In

SEO 427

Abstract

We present a solution of the Lachlan problem on the existence of stable Ehrenfeucht theories, and syntactic generic constructions as keys for the classification of countable models of complete theories with respect to two basic characteristics: Rudin-Keisler preorders and distribution functions for limit models. As a result we obtain a classification of countable models (up to the continuum hypothesis) for the class of Ehrenfeucht theories, for the class of small theories, and for the class of theories with continuum many types (the last one is joint with Roman Popkov).