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

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

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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DOI 10.2178/jsl/1120224733
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References found in this work BETA

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 Pure and Applied Logic 2 (1):69.

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Tameness and Extending Frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.

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