Sherwood Hachtman : Guessing and trees around singular cardinals

Posted by Sherwood Hachtman , part of the Logic Seminar.

At

Oct. 30, 2018, 3:30 p.m.

In

427 SEO

Abstract

Guessing principles assert the existence of elementary submodels of levels of $V$ with a great deal of absoluteness. These characterize large cardinals, but can consistently hold for small cardinals (like $\aleph_2$) as well. Their close relatives, the strong and super tree properties, share this characteristic; but while guessing principles have a number of combinatorial consequences (e.g. for failures of square, approachability, and the SCH), the case with these tree properties is less clear. We will introduce all of these principles with a minimum of prerequisites, and discuss a number of results concerning the extent to which guessing models and the super tree property can hold near a singular. This is joint work with Dima Sinapova.