Stability in abstract elementary classes of modules

Abstract: 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.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.