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- Tapani Hyttinen, Jouko A. Väänänen
- J. Symb. Log.
- 1990

- Tapani Hyttinen, Olivier Lessmann
- J. Symb. Log.
- 2002

- Tapani Hyttinen, Heikki Tuuri
- Ann. Pure Appl. Logic
- 1991

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)

- Tapani Hyttinen
- Arch. Math. Log.
- 2000

- Tapani Hyttinen
- Notre Dame Journal of Formal Logic
- 1995

- Tapani Hyttinen
- Math. Log. Q.
- 2002

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)

- Tapani Hyttinen, Meeri Kesälä
- Ann. Pure Appl. Logic
- 2006

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)

- Tapani Hyttinen, Saharon Shelah
- Ann. Pure Appl. Logic
- 2000

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)