Marcos Mazari-Armida (Carnegie Mellon University), Stability in abstract elementary classes of modules

Tue, 13 April 2021, 1 pm MDT

Abstract elementary classes (AECs for short) were introduced by Shelah in the seventies to study those classes of structures that can not be axiomatized by a first-order theory. In this talk, we will introduce the basic notions of AECs and showcase them in classes of modules. In particular, we will explore if every AEC of modules with pure embeddings is stable. Using that the class of p-groups with pure embeddings is a stable AEC, we will present a solution to a problem of László Fuchs.

[slides] [video]