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2010 Indestructible Strong Unfoldability
Joel David Hamkins, Thomas A. Johnstone
Notre Dame J. Formal Logic 51(3): 291-321 (2010). DOI: 10.1215/00294527-2010-018

Abstract

Using the lottery preparation, we prove that any strongly unfoldable cardinal κ can be made indestructible by all < κ -closed κ + -preserving forcing. This degree of indestructibility, we prove, is the best possible from this hypothesis within the class of < κ -closed forcing. From a stronger hypothesis, however, we prove that the strong unfoldability of κ can be made indestructible by all < κ -closed forcing. Such indestructibility, we prove, does not follow from indestructibility merely by < κ -directed closed forcing. Finally, we obtain global and universal forms of indestructibility for strong unfoldability, finding the exact consistency strength of universal indestructibility for strong unfoldability.

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Joel David Hamkins. Thomas A. Johnstone. "Indestructible Strong Unfoldability." Notre Dame J. Formal Logic 51 (3) 291 - 321, 2010. https://doi.org/10.1215/00294527-2010-018

Information

Published: 2010
First available in Project Euclid: 18 August 2010

zbMATH: 1207.03057
MathSciNet: MR2675684
Digital Object Identifier: 10.1215/00294527-2010-018

Subjects:
Primary: 03E40, 03E55

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 3 • 2010
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