Superstability and Symmetry

Abstract

This paper continues the study of superstability in abstract elementary classes (AECs) satisfying the amalgamation property. In particular, we consider the definition of $\mu$-superstability which is based on the local character characterization of superstability from first order logic. Not only is $\mu$-superstability a potential dividing line in the classification theory for AECs, but it is also a tool in proving instances of Shelah's Categoricity Conjecture. In this paper, we introduce a formulation, involving towers, of symmetry over limit models for $\mu$-superstable abstract elementary classes. We use this formulation to gain insight into the problem of the uniqueness of limit models for categorical AECs.

Accepted for publication by Annals of Pure and Applied Logic

References in corpus (2)

• Symmetry and the Union of Saturated Models in Superstable Abstract Elementary Classes
• A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes