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

Journal of Symbolic Logic 70 (2):639 - 660 (2005)
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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Saharon Shelah (1970). Finite Diagrams Stable in Power. Annals of Mathematical Logic 2 (1):69-118.

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