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Universal indestructibility for degrees of supercompactness and strongly compact cardinals

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Abstract

We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which exhibits a significant amount of indestructibility for its strong compactness.

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Authors and Affiliations

  1. Department of Mathematics, Baruch College of CUNY, New York, NY, 10010, USA

    Arthur W. Apter

  2. Department of Mathematics, The CUNY Graduate Center, 365 Fifth Avenue, New York, NY, 10016, USA

    Arthur W. Apter

  3. Group in Logic and the Methodology of Science, University of California, Berkeley, CA, 94720, USA

    Grigor Sargsyan

Authors
  1. Arthur W. Apter
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  2. Grigor Sargsyan
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Correspondence to Arthur W. Apter.

Additional information

The first author’s research was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive grants. The first author wishes to thank James Cummings for helpful discussions on the subject matter of this paper. In addition, both authors wish to thank the referee, for many helpful comments and suggestions which were incorporated into the current version of the paper.

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Apter, A.W., Sargsyan, G. Universal indestructibility for degrees of supercompactness and strongly compact cardinals. Arch. Math. Logic 47, 133–142 (2008). https://doi.org/10.1007/s00153-008-0072-8

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  • DOI: https://doi.org/10.1007/s00153-008-0072-8

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