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J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, p. 291–321, 2010.
[Bibtex]@ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability, AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.}, TITLE = {Indestructible strong unfoldability}, JOURNAL = {Notre Dame Journal of Formal Logic}, FJOURNAL = {Notre Dame Journal of Formal Logic}, VOLUME = {51}, YEAR = {2010}, NUMBER = {3}, PAGES = {291--321}, ISSN = {0029-4527}, MRCLASS = {03E55 (03E40)}, MRNUMBER = {2675684 (2011i:03050)}, MRREVIEWER = {Bernhard A. König}, DOI = {10.1215/00294527-2010-018}, URL = {http://jdh.hamkins.org/indestructiblestrongunfoldability/}, file = F, }
Using the lottery preparation, we prove that any strongly unfoldable cardinal $\kappa$ can be made indestructible by all ${\lt}\kappa$-closed + $\kappa^+$-preserving forcing. This degree of indestructibility, we prove, is the best possible from this hypothesis within the class of ${\lt}\kappa$-closed forcing. From a stronger hypothesis, however, we prove that the strong unfoldability of $\kappa$ can be made indestructible by all ${\lt}\kappa$-closed forcing. Such indestructibility, we prove, does not follow from indestructibility merely by ${\lt}\kappa$-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.