Thomas Johnstone: Substituting Supercompactness by Strong Unfoldability

Week 1, Monday June 15, 16:30-16:55

Strongly unfoldable cardinals are relatively low in the hierarchy of large cardinals, they lie well below measurable cardinals and are consistent with V=L. In this talk I will discuss recent results that have shown how strong unfoldability can serve as a highly efficient substitute for supercompactness in several large cardinal phenomena. In particular, I will discuss a Laver-like indestructibility theorem for strong unfoldability and a Baumgartner-like relative consistency proof of a fragment PFA: If kappa is a strongly unfoldable cardinal, then there is a model in which kappa is indestructible by all <kappa-closed, kappa^+ preserving forcing notions; and there is a model in which PFA holds for forcing notions that preserve either aleph_2 or aleph_3.
This is joint work with Joel David Hamkins.