# Franklin Tall: PFA(S)[S] and copies of $\omega_1$

Place: Fields Institute (Room 210)

Date: July 17th, 2015 (13:30-15:00)

Speaker: Franklin Tall

Title: PFA(S)[S] and copies of $\omega_1$

Abstract:

Alan Dow proved PFA(S)[S] implies every first countable perfect preimage of $\omega_1$ includes a copy of $\omega_1$. This plus a variation of P-ideal Dichotomy were the last things needed to prove PFA(S)[S] implies hereditarily normal manifolds of dim > 1 are metrizable. In conjunction with other consequences of PFA(S)[S], Dow’s work enables me to prove various new consistency results for sequentially compact spaces. I will talk about these today and also try to give some intuition behind his proof. The details will be given at some later date.