Maxwell Levine : Stationary Sets Added When Forcing Square Sequences

Posted by James Freitag , part of the Logic Seminar.

At

Jan. 31, 2017, 4 p.m.

In

SEO 427

Abstract

Current research in singular cardinal combinatorics emphasizes the tension between the reflection properties entailed by large cardinals and the combinatorial properties of Gödel's constructible universe, notably the square principle that was isolated by Jensen. In order to analyze this tension we construct models that exhibit some reflection properties while still satisfying weakenings of the square property. This presents a technical hurdle because the standard forcing techniques for adding square sequences also add non-reflecting stationary sets. In this talk we will look at why this happens.