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Level by Level Inequivalence, Strong Compactness, and GCH

Volume 60 / 2012

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 60 (2012), 201-209 MSC: 03E35, 03E55. DOI: 10.4064/ba60-3-1

Abstract

We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal $\kappa $, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.

Authors

  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.
    and
    The CUNY Graduate Center, Mathematics
    365 Fifth Avenue
    New York, NY 10016, U.S.A.
    e-mail

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