Large cardinals with few measures
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- by Arthur W. Apter, James Cummings and Joel David Hamkins PDF
- Proc. Amer. Math. Soc. 135 (2007), 2291-2300 Request permission
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.References
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Additional Information
- Arthur W. Apter
- Affiliation: Department of Mathematics, Baruch College of CUNY, New York, New York 10010
- MR Author ID: 26680
- Email: awapter@alum.mit.edu
- James Cummings
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- MR Author ID: 289375
- ORCID: 0000-0002-7913-0427
- Email: jcumming@andrew.cmu.edu
- Joel David Hamkins
- Affiliation: Mathematics Program, The Graduate Center of The City University of New York, 365 Fifth Avenue, New York, New York 10016 — Department of Mathematics, The College of Staten Island of CUNY, Staten Island, New York 10314
- MR Author ID: 347679
- Email: jdh@hamkins.org
- Received by editor(s): March 14, 2006
- Published electronically: March 2, 2007
- Additional Notes: The research of the first and third authors was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive Grants. The second author’s research was partially supported by NSF Grant DMS-0400982.
- Communicated by: Julia Knight
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2291-2300
- MSC (2000): Primary 03E35, 03E55
- DOI: https://doi.org/10.1090/S0002-9939-07-08786-2
- MathSciNet review: 2299507