# Topic Archive: PFA

Set theory seminarFriday, March 18, 201610:00 amGC 6417

# wPFA

University of Münster

We isolate a new forcing axiom, ${\rm wPFA}$, which is strictly between ${\rm BPFA}$ and ${\rm PFA}$. ${\rm wPFA}$ is equiconsistent with a remarkable cardinal, it implies the failure of $\square_{\omega_1}$, but it is compatible with $\square_\kappa$ for all $\kappa \geq \omega_2$. This is part of joint work with J. Bagaria and V. Gitman.

Set theory seminarFriday, March 21, 201410:00 amGC6417

# A proof of the relative consistency of PFA

The CUNY Graduate Center

I will use a supercompact cardinal to force the Proper Forcing Axiom (PFA). I will follow Baumgartner’s original argumet, but will use lottery sums instead of a Laver function.

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.