Superstability in simple finitary AECs

• Autorzy: Tapani Hyttinen , Meeri Kesälä
• Języki publikacji: EN

Abstrakty

EN

We continue the study of finitary abstract elementary classes beyond ℵ₀-stability. We suggest a possible notion of superstability for simple finitary AECs, and derive from this notion several good properties for independence. We also study constructible models and the behaviour of Galois types and weak Lascar strong types in this context.
We show that superstability is implied by a-categoricity in a suitable cardinal. As an application we prove the following theorem: Assume that $(𝕂, ≼_𝕂)$ is a simple, tame, finitary AEC, a-categorical in some cardinal κ above the Hanf number such that cf(κ) > ω. Then $(𝕂, ≼_𝕂)$ is a-categorical in each cardinal above the Hanf number.

Kategorie tematyczne

• 03C95: Abstract model theory
• 03C52: Properties of classes of models
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 195
• Numer: 3
• Strony: 221-268

Daty

wydano

2007

Twórcy

autor

Tapani Hyttinen

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland

autor

Meeri Kesälä

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland

Identyfikatory

DOI

10.4064/fm195-3-3