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arXiv · 1407.6335

Large cardinals need not be large in HOD

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.

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Yong Cheng, Sy-David Friedman, Joel David Hamkins. 2014-07-23. Large cardinals need not be large in HOD. https://arxiv.org/abs/1407.6335

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