Large cardinals with few measures

Arthur W. Apter; James Cummings; Joel David Hamkins

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Large cardinals with few measures

Arthur W. Apter·James Cummings·Joel David Hamkins

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Abstract

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods generalize to higher cardinals, showing that the number of lambda strong compactness or lambda supercompactness measures on P_kappa(lambda) can be exactly lambda+, if lambda>kappa is a regular cardinal. We conclude with a list of open questions. Our proofs use a critical observation due to James Cummings.

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BibTeX RIS

Arthur W. Apter, James Cummings, Joel David Hamkins. 2006-03-12. Large cardinals with few measures. https://arxiv.org/abs/math/0603260

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