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Upward categoricity from a successor cardinal for tame abstract classes with amalgamation

Published online by Cambridge University Press:  12 March 2014

Olivier Lessmann
Olivier Lessmann*
Affiliation:
Mathematical Institute, Oxford University, Oxford, OX1 3LB., U.K., E-mail: lessniann@maths.ox.ac.uk
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Abstract

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 639 - 660
Copyright
Copyright © Association for Symbolic Logic 2005

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