Kurt Gödel Research Center

Miniworkshop June 2012

On the consistency strength of PFA

Talk given by S.-D.Friedman

Abstract

A long-standing open question is whether Baumgartner's result Con(supercompact) implies Con(PFA) can be reversed. The traditional approach to this problem is core model theory, which at present cannot yield consistency strengths past Woodin cardinals. In joint work with Peter Holy, based on some earlier work of Neeman, I'll show that it is consistent that there is a proper class of subcompact cardinals with PFA failing in all proper forcing extensions of the universe. This "quasi lower bound" provides some evidence that the consistency strength of PFA is beyond subcompactness. I'll also mention analogous work of Viale-Weig, which is based on entirely different methods.