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ON THE COFINALITY OF THE LEAST $\lambda $-STRONGLY COMPACT CARDINAL
Published online by Cambridge University Press: 19 January 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic