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Identity crises and strong compactness

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter  and
James Cummings
Arthur W. Apter
Affiliation:
Department of Mathematics, Baruch College of Cuny, New York, New York 10010, USA, E-mail:awabb@cunyvm.cuny.edu
James Cummings
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, USA, E-mail:jcumming+@andrew.cmu. edu
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Abstract

Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals k1..…kn are so that ki; for i = 1..…n is both the ith measurable cardinal and supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.

Keywords

Strongly compact cardinalsupercompact cardinalmeasurable cardinalidentity crisisreverse Easton iteration
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1895 - 1910
Copyright
Copyright © Association for Symbolic Logic 2000

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