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Superdestructibility: A dual to Laver's indestructibility

Published online by Cambridge University Press:  12 March 2014

Joel David Hamkins
Mathematics 15-215, City University of New York, College of Staten Island, 2800 Victory BLVD, Staten Island, New York 10314, USA, E-mail: Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Saharon Shelah
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 80903, USA, E-mail:


After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ.

Research Article
Copyright © Association for Symbolic Logic 1998

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[1] Hamkins, Joel David, Small forcing makes any cardinal superdestructible, to appear in this Journal.Google Scholar
[2] Ketonen, Jussi, Strong compactness and other cardinal sins, Annals of Mathematical Logic, vol. 5 (1972), pp. 4776.Google Scholar
[3] Laver, Richard, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol, 29 (1978), pp. 385388.10.1007/BF02761175Google Scholar