James Hanson : Strongly minimal sets in continuous logic

Posted by John Baldwin , part of the Logic Seminar.

At

Oct. 9, 2019, 3 p.m.

In

427 SEO

Abstract

The precise structural understanding of uncountably categorical theories given by the proof of the Baldwin-Lachlan theorem is known to fail in continuous logic in the context of inseparably categorical theories. The primary obstacle is the absence of strongly minimal sets in some inseparably categorical theories. We will develop the concept of strongly minimal sets in continuous logic and discuss some common conditions under which they are present in an $\omega$-stable theory. We will also examine the extent to which we recover a Baldwin-Lachlan style characterization in the presence of strongly minimal sets, and the issue of the number of separable models of an inseparably categorical theory.