Universal indestructibility

  • A. W.~Apter and J. D. Hamkins, “Universal indestructibility,” Kobe Journal Math, vol. 16, iss. 2, pp. 119-130, 1999.  
    @article {ApterHamkins99:UniversalIndestructibility,
    AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
    TITLE = {Universal indestructibility},
    JOURNAL = {Kobe Journal Math},
    FJOURNAL = {Kobe Journal of Mathematics},
    VOLUME = {16},
    YEAR = {1999},
    NUMBER = {2},
    PAGES = {119--130},
    ISSN = {0289-9051},
    MRCLASS = {03E55 (03E35)},
    MRNUMBER = {1745027 (2001k:03112)},
    MRNUMBER = {1 745 027},
    eprint = {math/9808004},
    archivePrefix = {arXiv},
    primaryClass = {math.LO},
    }

From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed closed forcing. Such a state of affairs is impossible with two supercompact cardinals or even with a cardinal which is supercompact beyond a measurable cardinal.

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