{{menu|Events|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.