Abstract
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.
Publisher
Cambridge University Press (CUP)
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