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.
Combinatorial Principles Related to Adding Clubs
14.06.2005 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25