Maxwell Levine : Weak Squares and Very Good Scales

Posted by Sherwood Hachtman , part of the Logic Seminar.

At

April 19, 2016, 4 p.m.

In

SEO 427

Abstract

The combinatorial properties of large cardinals tend to clash with those satisfied by Gödel's constructible universe, especially the square property (denoted $\square_\kappa$) isolated by Jensen in the seventies. Strong cardinal axioms refute the existence of square, but it is possible with some fine-tuning to produce models that exhibit some large cardinal properties together with weakenings of square. In this talk we will exhibit some results along these lines and will outline the techniques used to produce them.