18/January/2013, 13:30–15:00

Fields institute,Room 210

Speaker: Frank Tall

Title: More topological consequences of PFA(S)[S]

Abstract: It is useful to have consequences of PFA and V = L in the same model. Models of the form PFA(S)[S], obtained by forcing with a coherent Souslin tree S over models of PFA restricted to posets that preserve S, have been used by Todorcevic, Larson, and myself to solve a number of classic problems in topology. The proofs do not use much topology; the methods ought to have consequences in other areas of mathematics. My first talk will be mainly topological, but I will handwave at the set-theoretic arguments for the benefit of those who have previously sat through too many talks of mine on the subject . In my second talk, I will go through some of the noteworthy details of the new proofs that I have not previously given in the seminar. If there is demand by people who have not previously been exposed to the subject, I can arrange a seminar at some point to go through the details of the basic setup, which I do not want to do again in the regular seminar. In the current series of talks, I will be talking about a method for forcing a suitable set of size aleph_1 to be the union of countably many “small” subsets. I also hope to present a proof that it is consistent that there are no separable, hereditarily normal, first countable Dowker spaces. (A Dowker space is a normal space X such that X x [0,1] is not normal.)