# 2005 seminar talk: Combinatorial Principles Related to Adding Clubs

Talk held by John Krueger (KGRC) at the KGRC seminar on 2005-06-14.

### Abstract

A number of forcing posets have been defined which introduce a club subset to a given fat stationary subset of $\omega_2$ under various assumptions. I introduce a combinatorial property of $\omega_2$ which implies there exists a fat stationary subset of $\omega_2$ which cannot acquire a club subset by any forcing poset which preserves $\omega_1$ and $\omega_2$, answering a problem of Abraham and Shelah. This property follows from Martin's Maximum and is equiconsistent with a Mahlo cardinal.