Universal Indestructibility is Consistent with Two Strongly Compact Cardinals

Volume 53 / 2005

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 53 (2005), 131-135 MSC: 03E35, 03E55. DOI: 10.4064/ba53-2-2


We show that universal indestructibility for both strong compactness and supercompactness is consistent with the existence of two strongly compact cardinals. This is in contrast to the fact that if $\kappa$ is supercompact and universal indestructibility for either strong compactness or supercompactness holds, then no cardinal $\lambda > \kappa$ is measurable.


  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.

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