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Gap Forcing: Generalizing the Lévy-Solovay Theorem

Published online by Cambridge University Press:  15 January 2014

Joel David Hamkins
Joel David Hamkins*
Affiliation:
Department of Mathematics, City University of New York, College of Staten Island, 2800 Victory Boulevard, Staten Island, NY 10314, USAE-mail:hamkins@math.csi.cuny.edu
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Abstract

The Lévy-Solovay Theorem[8] limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that many of the forcing iterations most commonly found in the large cardinal literature create no new weakly compact cardinals, measurable cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost huge cardinals, huge cardinals, and so on.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 5 , Issue 2 , June 1999 , pp. 264 - 272
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

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