Critical Cardinals
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Hayut, Yair and Karagila, Asaf (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 |
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Faculty \ School: | Faculty of Science > School of Mathematics |
Related URLs: | |
Depositing User: | LivePure Connector |
Date Deposited: | 30 May 2019 14:30 |
Last Modified: | 09 Jan 2021 01:00 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/71176 |
DOI: | 10.1007/s11856-020-1998-8 |
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