Arthur W. Apter, James Cummings, Joel David Hamkins
Published 2006-03-12Version 1
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.
Large Cardinals and Definable Well-Orderings of the Universe
Low level definability above large cardinals
The large cardinals between supercompact and almost-huge
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