Notre Dame Journal of Formal Logic

Indestructible Strong Unfoldability

Joel David Hamkins and Thomas A. Johnstone

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 51, Number 3 (2010), 291-321.

Dates
First available in Project Euclid: 18 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1282137984

Digital Object Identifier
doi:10.1215/00294527-2010-018

Mathematical Reviews number (MathSciNet)
MR2675684

Zentralblatt MATH identifier
1207.03057

Subjects
Primary: 03E55: Large cardinals 03E40: Other aspects of forcing and Boolean-valued models

Keywords
strongly unfoldable cardinal forcing indestructibility

Citation

Hamkins, Joel David; Johnstone, Thomas A. Indestructible Strong Unfoldability. Notre Dame J. Formal Logic 51 (2010), no. 3, 291--321. doi:10.1215/00294527-2010-018. https://projecteuclid.org/euclid.ndjfl/1282137984


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References

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Notre Dame Journal of Formal Logic

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