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ToolsYou, Zhixing and Yuan, Jiachen (2023) On the cofinality of the least λ-strongly compact cardinal. Journal of Symbolic Logic. ISSN 0022-4812
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Abstract
In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.
| Item Type: | Article |
|---|---|
| Additional Information: | Funding Information: During the work, the first author was supported by NSFC No. 11871464 until July 2022 and the China Scholarship Council (No. 202004910742) from October 2020 to October 2021. The first author was also supported by the European Research Council (grant agreement ERC-2018-StG 802756) from July 2022. The second author was supported by UKRI Future Leaders Fellowship [MR/T021705/2]. |
| Uncontrolled Keywords: | cofinality,iterated ultrapower,radin forcing,λ-strongly compact cardinal,philosophy,logic ,/dk/atira/pure/subjectarea/asjc/1200/1211 |
| Faculty \ School: | Faculty of Science > School of Mathematics |
| UEA Research Groups: | Faculty of Science > Research Groups > Logic |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 20 Feb 2023 15:30 |
| Last Modified: | 27 Feb 2023 10:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/91204 |
| DOI: | 10.1017/jsl.2023.4 |
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