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An equiconsistency for universal indestructibility

  • Arthur W. Apter (a1) (a2) and Grigor Sargsyan (a3)

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.

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Corresponding author

Department of Mathematics, University of California, Los Angeles, CA 90095, USA, E-mail: grigor@math.ucla.edu., URL: http://www.math.ucla.edu/~grigor

References

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[1] Apter, A. and Hamkins, J. D., Universal indestructibility, Kobe Journal of Mathematics, vol. 16 (1999), pp. 119130.
[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. 16.
[3] Baldwin, S., Between strong and superstrong, this Journal, vol. 51 (1986), pp. 547559.
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[7] Hamkins, J. D., Gap forcing, Israel Journal of Mathematics, vol. 125 (2001), pp. 237252.
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[10] Steel, J., The core model iterability problem, Lecture Notes in Logic, vol. 8, Springer-Verlag, Berlin and New York, 1996.
[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.

Keywords

An equiconsistency for universal indestructibility

  • Arthur W. Apter (a1) (a2) and Grigor Sargsyan (a3)

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