Monica VanDieren : Superstability in AECs

Posted by Kostyantyn Slutskyy , part of the Logic Seminar.

At

Nov. 12, 2015, 4 p.m.

In

SEO 427

Abstract

In the 1970s Saharon Shelah initiated a program of generalizing first order model theoretic results to the setting of abstract elementary classes (AECs). Progress has been slow due in part to the difficulty of working without the compactness theorem. In this talk we will survey some of the recent developments in understanding superstability in AECs. In particular, we will discuss the relationship between symmetry and the uniqueness of limit models, and we will sketch the proof that in suitably superstable AECs the union of an increasing chain of saturated models is saturated.