| In the introduction and Chapter 2 we introduce various conditions which could potentially define "superstability" for abstract elementary classes. In particular, we examine various notions of "superlimit" model" and "superlimit class" which we will apply toward proving gap-transfer theorems for AECs. In Chapter 3 we examine Lessmann's analogue of Vaught's Theorem for abstract elementary classes. We provide a sufficient condition for the construction of an (LS(K)+, LS(K))-model. In Chapter 4 we discuss progress that has been made in proving uniqueness of limit models from various superstability assumptions. In Chapter 5 we give a sufficient condition, or perhaps more accurately, various sufficient conditions for the existence of an (N2, N0)-model to exist, using the existence of a simplified morass. Our work here is guided by the presentation of Jensen's work in proving the classical gap-2 transfer result for first order logic in (Devlin, 1984). |
