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arXiv:1407.6335 [math.LO]AbstractReferencesReviewsResources

Large cardinals need not be large in HOD

Yong Cheng, Sy-David Friedman, Joel David Hamkins

Published 2014-07-23, updated 2015-07-03Version 2

We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal $\kappa$ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in $V$, none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals.

Comments: 20 pages. Commentary concerning this article can be made at http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod
Categories: math.LO
Subjects: 03E55, 03E45
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