Dima Sinapova : Compactness and the failure of SCH

Posted by Dima Sinapova , part of the Logic Seminar.

At

Nov. 6, 2018, 3:30 p.m.

In

427 SEO

Abstract

There is a natural tension between violating SCH and compactness properties such as square, the tree property and its strengthenings. On the other hand, in order to obtain compactness at many cardinals simultaneously, we need many failures of SCH. A key questions is if a certain compactness property can hold at $\kappa^+$ for a singular $\kappa$ where SCH fails. I will go over some known facts, and then discuss a recent result on ITP and failure of SCH.