Upward Categoricity from a Successor Cardinal for Tame Abstract Classes with Amalgamation

Journal of Symbolic Logic 70 (2):639 - 660 (2005)
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Abstract

This paper is devoted to the proof of the following upward categoricity theorem: Let K be a tame abstract elementary class with amalgamation, arbitrarily large models, and countable Löwenheim-Skolem number. If K is categorical in ‮א‬₁ then K is categorical in every uncountable cardinal. More generally, we prove that if K is categorical in a successor cardinal λ⁺ then K is categorical everywhere above λ⁺

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10.2178/jsl/1120224733

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Citations of this work

Tameness and extending frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.
Abstract elementary classes stable in ℵ0.Saharon Shelah & Sebastien Vasey - 2018 - Annals of Pure and Applied Logic 169 (7):565-587.

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References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Toward categoricity for classes with no maximal models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.
Amalgamation properties and finite models in L n -theories.John Baldwin & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (2):155-167.
Finite diagrams stable in power.Saharon Shelah - 1970 - Annals of Mathematical Logic 2 (1):69-118.

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