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Mixed Levels of Indestructibility

Tom 63 / 2015

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 63 (2015), 113-122 MSC: 03E35, 03E55. DOI: 10.4064/ba63-2-2

Streszczenie

Starting from a supercompact cardinal , we force and construct a model in which \kappa is both the least strongly compact and least supercompact cardinal and \kappa exhibits mixed levels of indestructibility. Specifically, \kappa 's strong compactness, but not its supercompactness, is indestructible under any \kappa -directed closed forcing which also adds a Cohen subset of \kappa . On the other hand, in this model, \kappa 's supercompactness is indestructible under any \kappa -directed closed forcing which does not add a Cohen subset of \kappa .

Autorzy

  • 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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