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Superdestructibility: A dual to Laver's indestructibility

Published online by Cambridge University Press:  12 March 2014

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

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 549 - 554
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[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. 47–76.Google Scholar
[3] Laver, Richard, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol, 29 (1978), pp. 385–388.10.1007/BF02761175Google Scholar