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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


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.


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

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