Indestructible strong unfoldability

[bibtex key=HamkinsJohnstone2010:IndestructibleStrongUnfoldability]

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.

Leave a Reply

Your email address will not be published. Required fields are marked *