# 2013 seminar talk: More on the tree property

Talk held by Radek Honzik (KGRC) at the KGRC seminar on 2013-05-02.

### Abstract

More than a Woodin cardinal is required to obtain tree property at two adjacent cardinals. We make a first step toward showing that a much weaker assumption is sufficient for the tree property to hold at all even successor cardinals. Specifically, we show that from $\omega$-many weak compacts one can obtain the tree property at all of the $\aleph_{2n}$'s and from a cardinal which is strong up to a larger weak compact one can in addition have the tree property at $\aleph_{\omega+2}$ ($\aleph_\omega$ strong limit).

This work is joint with Sy-D. Friedman.