# Topic Archive: strongly unfoldable cardinal

Set theory seminarFriday, March 7, 201410:00 amGC6417

# The consistency strength of PFA for posets preserving aleph_2 or aleph_3

The CUNY Graduate Center

While the consistency strength of PFA is quite high in the large cardinal hierarchy, it is reasonable to expect that tame fragments of PFA should require much weaker assumptions. I will present an argument of Hamkins and Johnstone (2008) which shows the consistency of PFA for posets preserving aleph_2 or aleph_3 from a strongly unfoldable cardinal, a much smaller large cardinal which is, roughly speaking, to strongness (or supercompactness) as weak compactness is to measurability.