Sean Cox : Indestructible guessing models

Posted by Dima Sinapova , part of the Logic Seminar.

At

Feb. 9, 2016, 4 p.m.

In

SEO 427

Abstract

By results of Viale-Weiss, stationarity of the class of "guessing models" is responsible for many of the consequences of the Proper Forcing Axiom (PFA), including the Tree Property at $\omega_2$ and failure of square. I will discuss joint work with Krueger about the stronger notion of "indestructible guessing models". Stationarity of such models captures even more consequences of PFA (e.g. Suslin's Hypothesis, SCH, and a theorem of Todorcevic), but on the other hand doesn't decide the value of the continuum.