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September 2011 Categoricity transfer in simple finitary abstract elementary classes
Tapani Hyttinen, Meeri Kesälä
J. Symbolic Logic 76(3): 759-806 (September 2011). DOI: 10.2178/jsl/1309952520

Abstract

We continue our study of finitary abstract elementary classes, defined in [7]. In this paper, we prove a categoricity transfer theorem for a case of simple finitary AECs. We introduce the concepts of weak κ-categoricity and f-primary models to the framework of ℵ0-stable simple finitary AECs with the extension property, whereby we gain the following theorem: Let (𝕂,≼𝕂) be a simple finitary AEC, weakly categorical in some uncountable κ. Then (𝕂,≼𝕂) is weakly categorical in each λ≥min{κ,ℶ(20)+}. If the class (𝕂,≼𝕂) is also LS(𝕂)-tame, weak κ-categoricity is equivalent with κ-categoricity in the usual sense.

We also discuss the relation between finitary AECs and some other non-elementary frameworks and give several examples.

Citation

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Tapani Hyttinen. Meeri Kesälä. "Categoricity transfer in simple finitary abstract elementary classes." J. Symbolic Logic 76 (3) 759 - 806, September 2011. https://doi.org/10.2178/jsl/1309952520

Information

Published: September 2011
First available in Project Euclid: 6 July 2011

zbMATH: 1250.03055
MathSciNet: MR2849245
Digital Object Identifier: 10.2178/jsl/1309952520

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 3 • September 2011
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