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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 ∪… (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)

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

We show that the excellence axiom in the definition of Zilber’s quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies a number of categoricity proofs.

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

- Åsa Hirvonen, Tapani Hyttinen
- Arch. Math. Log.
- 2009

We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation,… (More)

- Tapani Hyttinen, Olivier Lessmann
- Ann. Pure Appl. Logic
- 2006

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

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