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Title: Strong compactness and the ultrapower axiom I: the least strongly compact cardinal
The Ultrapower Axiom is a combinatorial principle concerning the structure of large cardinals that is true in all known canonical inner models of set theory. A longstanding test question for inner model theory is the equiconsistency of strongly compact and supercompact cardinals. In this paper, it is shown that under the Ultrapower Axiom, the least strongly compact cardinal is supercompact. A number of stronger results are established, setting the stage for a complete analysis of strong compactness and supercompactness under UA that will be carried out in the sequel to this paper.  more » « less
Award ID(s):
1902884
PAR ID:
10472497
Author(s) / Creator(s):
Publisher / Repository:
World Scientific
Date Published:
Journal Name:
Journal of Mathematical Logic
Volume:
22
Issue:
02
ISSN:
0219-0613
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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