Midwest Model Theory Seminar
Marcos Mazari Armida
Carnegie Mellon
Stability and superstability in classes of modules
Abstract: Fisher and Baur showed in the seventies that if T is a complete first-order theory extending the theory of modules, then the class of models of T with pure embeddings is stable. In this talk we will explore if the same holds for any abstract elementary class of modules, i.e., for any AEC (K, <_p) such that K is a class of R-modules for a fixed ring R and <_p is the pure submodule relation. In particular, using that the class of p-groups with pure embeddings is a stable AEC, I will present a solution to a problem of L. Fuchs. Moreover, we will study the notion of superstability and show how superstability can be used to give new characterizations of some classical rings.
Please write jfreitag@uic.edu for login information for the seminar.
Tuesday March 23, 2021 at 4:00 PM in the internet