Critical Cardinals

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Hayut, Yair and Karagila, Asaf ORCID: https://orcid.org/0000-0003-1289-0904 (2020) Critical Cardinals. Israel Journal of Mathematics, 236 (1). 449–472. ISSN 0021-2172

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Abstract

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings to symmetric extensions, and we use this to show that it is consistent relative to a supercompact cardinal that there is a critical cardinal whose successor is singular.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1805.02533
Depositing User:	LivePure Connector
Date Deposited:	30 May 2019 14:30
Last Modified:	22 Oct 2022 04:47
URI:	https://ueaeprints.uea.ac.uk/id/eprint/71176
DOI:	10.1007/s11856-020-1998-8

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