Strong compactness, measurability, and the class of supercompact cardinals

Volume 167 / 2001

Arthur W. Apter Fundamenta Mathematicae 167 (2001), 65-78 MSC: 03E35, 03E55. DOI: 10.4064/fm167-1-5


We prove two theorems concerning strong compactness, measurability, and the class of supercompact cardinals. We begin by showing, relative to the appropriate hypotheses, that it is consistent non-trivially for every supercompact cardinal to be the limit of (non-supercompact) strongly compact cardinals. We then show, relative to the existence of a non-trivial (proper or improper) class of supercompact cardinals, that it is possible to have a model with the same class of supercompact cardinals in which every measurable cardinal $\delta $ is $2^\delta $ strongly compact.


  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.

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