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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: [email protected], 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: [email protected], URL: http://math.berkeley.edu/~grigor
*
Department of Mathematics, University of California, Los Angeles, CA 90095, USA, E-mail: [email protected]., 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

[1] Apter, A. and Hamkins, J. D., Universal indestructibility, Kobe Journal of Mathematics, vol. 16 (1999), pp. 119–130.Google Scholar
[2] Apter, A. and Sargsyan, G., A reduction in consistency strength for universal indestructibility, Bulletin of the Polish Academy of Sciences (Mathematics), vol. 55 (2007), pp. 1–6.Google Scholar
[3] Baldwin, S., Between strong and superstrong, this Journal, vol. 51 (1986), pp. 547–559.Google Scholar
[4] Gitik, M. and Shelah, S., On certain indestructibility of strong cardinals and a question of Hajnal, Archive for Mathematical Logic, vol. 28 (1989), pp. 35–42.Google Scholar
[5] Hamkins, J. D., Gap forcing: Generalizing the Lévy-Solovay Theorem, The Bulletin of Symbolic Logic, vol. 5 (1999), pp. 264–272.Google Scholar
[6] Hamkins, J. D., The lottery preparation, Annals of Pure and Applied Logic, vol. 101 (2000), pp. 103–146.Google Scholar
[7] Hamkins, J. D., Gap forcing, Israel Journal of Mathematics, vol. 125 (2001), pp. 237–252.Google Scholar
[8] Kanamori, A., The higher infinite, Springer-Verlag, Berlin and New York, 1994.Google Scholar
[9] Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol. 29 (1978), pp. 385–388.Google Scholar
[10] Steel, J., The core model iterability problem, Lecture Notes in Logic, vol. 8, Springer-Verlag, Berlin and New York, 1996.Google Scholar
[11] Zeman, M.. Inner models and large cardinals, de Gruyter Series in Logic and its Applications, vol. 5, Walter de Gruyter and Co., Berlin, 2002.Google Scholar