Large cardinals with few measures
Logic
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0603260,
title = {Large cardinals with few measures},
author = {Arthur W. Apter and James Cummings and Joel David Hamkins},
journal= {arXiv preprint arXiv:math/0603260},
year = {2007}
}
Comments
15 pages