Uncountable categoricity of local abstract elementary classes with amalgamation

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Annals of Pure and Applied Logic 143 (1-3):29-42 (2006)
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Abstract

We give a complete and elementary proof of the following upward categoricity theorem: let be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable Löwenheim–Skolem number. If is categorical in 1 then is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in first order logic without any use of prime models or heavy stability theoretic machinery

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10.1016/j.apal.2006.01.007

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References found in this work

Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
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.
Finite variable logic, stability and finite models.Marko Djordjević - 2001 - Journal of Symbolic Logic 66 (2):837-858.

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