# Superdestructibility: a dual to Laver's indestructibility

• J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” Journal of Symbolic Logic, vol. 63, iss. 2, p. 549–554, 1998.
[Bibtex]
@article {HamkinsShelah98:Dual,
AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
JOURNAL = {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://jdh.hamkins.org/dual/},
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 $\kappa$.