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Mathematics > Logic

arXiv:1407.6335 (math)
[Submitted on 23 Jul 2014 (v1), last revised 3 Jul 2015 (this version, v2)]

Title:Large cardinals need not be large in HOD

Authors:Yong Cheng, Sy-David Friedman, Joel David Hamkins
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Abstract: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 this http URL
Subjects: Logic (math.LO)
MSC classes: 03E55, 03E45
Cite as: arXiv:1407.6335 [math.LO]
  (or arXiv:1407.6335v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1407.6335
Journal reference: Annals of Pure and Applied Logic, Volume 166, Issue 11, November 2015, Pages 1186-1198

Submission history

From: Joel David Hamkins [view email]
[v1] Wed, 23 Jul 2014 19:15:41 UTC (28 KB)
[v2] Fri, 3 Jul 2015 19:17:16 UTC (22 KB)
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