Using the lottery preparation, we prove that any strongly unfoldable cardinal can be made indestructible by all <-closed -preserving forcing. This degree of indestructibility, we prove, is the best possible from this hypothesis within the class of <-closed forcing. From a stronger hypothesis, however, we prove that the strong unfoldability of can be made indestructible by all <-closed forcing. Such indestructibility, we prove, does not follow from indestructibility merely by <-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.
"Indestructible Strong Unfoldability." Notre Dame J. Formal Logic 51 (3) 291 - 321, 2010. https://doi.org/10.1215/00294527-2010-018