Matteo Viale: Some questions on the models of MM

Week 1, Monday June 15, 09:15-09:40

We will briefly discuss some questions concerning the saturation properties of models of strong forcing axioms (MM, PFA, etc). Caicedo and Velickovic conjectured the following:
Assume MM and let W be an inner model with the same cardinals of the universe V. Then all sequences of ordinals of length aleph_1 are already elements of the inner model W.
We shall discuss the motivations and the ground for the above conjecture as well as some partial results relating the conjecture to certain Ramsey properties and to Shelah's pcf theory.