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ON CATEGORICITY IN SUCCESSIVE CARDINALS

Published online by Cambridge University Press:  20 July 2020

SEBASTIEN VASEY*
Affiliation:
RADIX TRADING LLC. CHICAGO, IL60654, USAE-mail:[email protected]: svasey.github.io

Abstract

We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb {L}_{\omega _1, \omega }$ sentence categorical on an end segment of cardinals below $\beth _\omega $ must be categorical also everywhere above $\beth _\omega $ . This is done without any additional model-theoretic hypotheses (such as amalgamation or arbitrarily large models) and generalizes to the much broader framework of tame AECs with weak amalgamation and coherent sequences.

Type
Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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