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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)
Saharon Shelah, in his recently published list of open problems in model theory [Sh 702], writes, " I see this [classification of Abstract Elementary Classes] as the major problem of model theory. " Shelah in the mid seventies proposed a categoricity conjecture as an easy to state but very difficult test problem. Shelah alone published many hundreds of(More)
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)