Kevin Zhou : An Overview of Abstract Elementary Classes

Posted by Kevin Zhou , part of the Louise Hay Logic Seminar.

At

Oct. 11, 2018, 4 p.m.

In

427 SEO

Abstract

Abstract Elementary Classes (AECs) were introduced by Shelah in 1987 as a generalization of elementary classes of first-order theories. Many interesting objects of study in model theory form nonelementary classes (e.g. Archimedean ordered fields, locally finite groups, etc.), but can be expressed in some stronger logic (e.g. infintary logics such as $L_{\omega_1,\omega}$, higher order logics, etc.); AECs provide a framework to study these classes in a more general setting. In this talk, I will present the basics of AECs, as well as some important results and open problems in the classification theory of AECs.