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Small forcing makes any cardinal superdestructible

Published online by Cambridge University Press:  12 March 2014

Joel David Hamkins
Joel David Hamkins*
Affiliation:
Mathematics 15-215, City University of New York, CSI, 2800 Victory Blvd., Staten Island, NY 10314, USA, E-mail: hamkins@integral.math.csi.cuny.edu
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Abstract

Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal κ becomes superdestructible—any further <κ-closed forcing which adds a subset to κ will destroy the measurability, even the weak compactness, of κ. Nevertheless, after small forcing indestructible cardinals remain resurrectible, but never strongly resurrectible.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 1 , March 1998 , pp. 51 - 58
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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