Superdestructibility: a dual to Laver's indestructibility

  • J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J.~Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ([HmSh:618])  
    @article {HamkinsShelah98:Dual,
    AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
    TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
    JOURNAL = {J.~Symbolic Logic},
    FJOURNAL = {The Journal of Symbolic Logic},
    VOLUME = {63},
    YEAR = {1998},
    NUMBER = {2},
    PAGES = {549--554},
    ISSN = {0022-4812},
    CODEN = {JSYLA6},
    MRCLASS = {03E55 (03E40)},
    MRNUMBER = {1625927 (99m:03106)},
    MRREVIEWER = {Douglas R.~Burke},
    DOI = {10.2307/2586848},
    URL = {http://dx.doi.org/10.2307/2586848},
    note = {[HmSh:618]},
    eprint = {math/9612227},
    archivePrefix = {arXiv},
    primaryClass = {math.LO},
    }

After small forcing, any $<\kappa$-closed forcing will destroy the supercompactness, even the strong compactness, of $\kappa$.

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  1. Pingback: Large cardinal indestructibility: two slick new proofs of prior results | Joel David Hamkins

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