Large cardinals with few measures

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
15 pages

Keywords

Logic, 03E35; 03E55

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/110148

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603260
 http://arxiv.org/abs/math/0603260

Collections

arXiv