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- 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)

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, Meeri Kesälä
- Notre Dame Journal of Formal Logic
- 2011

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, so called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore we give and example where… (More)

- Tapani Hyttinen, Meeri Kesälä
- Ann. Pure Appl. Logic
- 2012

We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable nitary abstract elementary classes: from a certain expression of `non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule… (More)

The paper studies the history and recent developments in non-elementary model theory focusing in the framework of abstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to non-elementary frameworks and illuminate the study with concrete examples of classes of models. This second… (More)

- Meeri Kesälä, Iris Tomaszewski, +5 authors Juha O. Viljanen
- 2006

elementary classes Shelah suggested in [26] abstract elementary classes (AEC) as a platform to study model theoretic concepts in a more general setting. He studies a class K of structures in a fixed similarity type τ , but does not define any specific language. Instead he gives axioms for (K,4K) , where 4K is a relation between the models of the class. The… (More)

- Tapani Hyttinen, Meeri Kesälä
- J. Symb. Log.
- 2011

We continue to study nitary abstract elementary classes, de ned in [7]. We introduce a concept of weak κ -categoricity and an f-primary model in a א0 -stable simple nitary AEC with the extension property, and gain the following theorem: Let (K,4K) be a simple nitary AEC, weakly categorical in some uncountable κ . Then (K,4K) is weakly categorical in each λ… (More)

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