Dima Sinapova : Singularizing and square

Posted by Dima Sinapova , part of the Logic Seminar.

At

April 9, 2019, 3:30 p.m.

In

427 SEO

Abstract

It is an old theorem that if a regular cardinal is singularized to have cofinality $\omega$, while preserving cardinals, then $\square_{\kappa, \omega}$ holds in the outer model. We will show that this does not generalize to uncountable cofinalities. In particular, we show that after the right kind of preparation, in the Magidor model of singularizing $\kappa$ to uncountable cofinality all intermediate forms of square at $\kappa$ fail. This is joint work with Maxwell Levine.