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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 |
| Related URLs: | |
| 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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