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In this paper we study a specific subclass of abstract elementary classes. We construct a notion of independence for these AEC's and show that under simplicity the notion has all the usual properties of first order non-forking over complete types. Our approach generalizes the context of ℵ0-stable homogeneous classes and excellent classes. Our set of… (More)

In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in [Hy]. We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see [Hy]. 1. Basic… (More)

We prove a main gap theorem for locally saturated submodels of a homogeneous structure. We also study the number of locally saturated models, which are not elementarily embeddable to each other. Through out this paper we assume that M is a homogeneous model of similarity type (=lan-guage) L. We study elementary submodels of M. We use M as the monster model… (More)

This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem: Theorem. Let C be a large homogeneous model of a stable diagram D. Let p, q ∈ SD(A), where p is quasiminimal and q unbounded. Let P = p(C) and Q = q(C). Suppose that there exists an integer n < ω such that dim(a1. .. an/A ∪ C)… (More)

We continue to study nitary abstract elementary classes, dened in [7]. We introduce a concept of weak κ-categoricity and an f-primary model in a ℵ 0-stable simple nitary AEC with the extension property, and gain the following theorem: Let (K, K) be a simple nitary AEC, weakly categorical in some uncountable κ. Then (K, K) is weakly categorical in each λ ≥… (More)