Large cardinals with few measures

Details Large cardinals with few measures Large cardinals with few measures

2006-03-12

arxiv.org/abs/math/0603260v1

Mathematics

Logic

15 pages

Scientific paper

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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