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Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

Volume 63 / 2015

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 63 (2015), 185-194 MSC: 03E35, 03E55. DOI: 10.4064/ba8014-12-2015 Published online: 14 December 2015


We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal $\kappa $ has its strong compactness indestructible under $\kappa $-directed closed forcing. This is in analogy to and generalizes the author’s result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.


  • 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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