Itay Neeman : The tree property

Posted by Dima Sinapova , part of the Logic Seminar.

At

April 22, 2014, 4 p.m.

In

SEO 427

Abstract

The tree property at $\kappa$ asserts that every tree of height $\kappa$ with levels of sizes less than $\kappa$ has a cofinal branch. At $\kappa=\aleph_0$ and $\kappa=\aleph_1$ the property and its negation (respectively) are well known classical results. We discuss methods to obtain the property at other cardinals, where it can be viewed as a delicate remnant of large cardinal strength.