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ON THE COFINALITY OF THE LEAST $\lambda $-STRONGLY COMPACT CARDINAL

Part of: Set theory

Published online by Cambridge University Press:  19 January 2023

ZHIXING YOU  and
JIACHEN YUAN
ZHIXING YOU
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE UNIVERSITY OF BARCELONA 08001, BARCELONA, SPAIN INSTITUTE OF MATHEMATICS ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE CHINESE ACADEMY OF SCIENCES, BEIJING 100190 PEOPLE’S REPUBLIC OF CHINA and SCHOOL OF MATHEMATICAL SCIENCES UNIVERSITY OF CHINESE ACADEMY OF SCIENCES BEIJING 100049, PEOPLE’S REPUBLIC OF CHINA Current address: DEPARTMENT OF MATHEMATICS BAR-ILAN UNIVERSITY RAMAT-GAN 5290002, ISRAEL E-mail: [email protected]
JIACHEN YUAN*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UK Current address: SCHOOL OF MATHEMATICS UNIVERSITY OF LEEDS LEEDS LS2 9JT, UK
*
E-mail: [email protected]
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Abstract

In this paper, we characterize the possible cofinalities of the least $\lambda $-strongly compact cardinal. We show that, on the one hand, for any regular cardinal, $\delta $, that carries a $\lambda $-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above $\delta $, that the least $\lambda $-strongly compact cardinal has cofinality $\delta $. On the other hand, provably the cofinality of the least $\lambda $-strongly compact cardinal always carries a $\lambda $-complete uniform ultrafilter.

Keywords

λ-strongly compact cardinalcofinalityiterated ultrapowerRadin forcing

MSC classification

Primary: 03E35: Consistency and independence results 03E55: Large cardinals
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 2 , June 2024 , pp. 569 - 582
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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