Superstability in simple finitary AECs

We continue the study of finitary abstract elementary classes beyond N(0)-stability. We suggest a possible notion of superstability for simple finitary AECs, and derive from this notion several good properties for independence. We also study constructible models and the behaviour of Galois types and weak Lascar strong types in this context. We show that superstability is implied by a-categoricity in a suitable cardinal. As an application we prove the following theorem: Assume that (K, <= K) is a simple, tame, finitary AEC, a-categorical in some cardinal kappa above the Hanf number such that cf (kappa) > omega. Then (K, <= K) is a-categorical in each cardinal above the Hanf number.