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An equiconsistency for universal indestructibility

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter  and
Grigor Sargsyan
Arthur W. Apter
Affiliation:
Department of Mathematics, Baruch college of CUNY, New York, NY 10010, USA The CUNY Graduate Center, Mathematics, 365 Fifth Av., New York, NY 10016, USA, E-mail: awapter@alum.mit.edu, URL: http://faculty.baruch.cuny.edu/apter
Grigor Sargsyan*
Affiliation:
Group in Logic and The Methodology of Science, University of California, Berkeley CA 94720, USA, E-mail: grigor@math.berkeley.edu, URL: http://math.berkeley.edu/~grigor
*
Department of Mathematics, University of California, Los Angeles, CA 90095, USA, E-mail: grigor@math.ucla.edu., URL: http://www.math.ucla.edu/~grigor
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Abstract

We obtain an equiconsistency for a weak form of universal indestructibility for strongness. The equiconsistency is relative to a cardinal weaker in consistency strength than a Woodin cardinal, Stewart Baldwin's notion of hyperstrong cardinal. We also briefly indicate how our methods are applicable to universal indestructibility for supercompactness and strong compactness.

Keywords

Universal indestructibilityindestructibilityequiconsistencymeasurable cardinalstrong cardinalhyperstrong cardinalWoodin cardinalstrongly compact cardinalsupercompact cardinalcore model
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 314 - 322
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

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