Dima Sinapova : Iteration, reflection, and Prikry forcing

Posted by Filippo Calderoni , part of the Logic Seminar.

At

Feb. 11, 2020, 3 p.m.

In

427 SEO

Abstract

There is an inherent tension between stationary reflection and the failure of SCH. The former is a compactness type principle that follows from large cardinals. The latter is an instance of incompactness, and usually obtained using Prikry forcing. We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.