2013 seminar talk: More on the tree property

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


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.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.