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June 2005 Upward categoricity from a successor cardinal for tame abstract classes with amalgamation
Olivier Lessmann
J. Symbolic Logic 70(2): 639-660 (June 2005). DOI: 10.2178/jsl/1120224733

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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Olivier Lessmann. "Upward categoricity from a successor cardinal for tame abstract classes with amalgamation." J. Symbolic Logic 70 (2) 639 - 660, June 2005. https://doi.org/10.2178/jsl/1120224733

Information

Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1089.03025
MathSciNet: MR2140051
Digital Object Identifier: 10.2178/jsl/1120224733

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 2 • June 2005
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