Series: Penn State Logic Seminar Date: Tuesday, February 13, 2007 Time: 2:30 - 3:45 PM Place: 106 McAllister Building Speaker: Natasha Dobrinen, University of Vienna, Mathematics Title: Co-stationarity of the ground model Abstract: Two-thirds of the work presented is joint with Sy-David Friedman. Given V and W models of ZFC with the same ordinals, where W contains V, and given kappa < lambda cardinals in W with kappa regular, let P_kappa(lambda) denote the collection of subsets of lambda of size less than kappa in W. We say that the ground model is co-stationary in P_kappa(lambda) if the collection of elements of P_kappa(lambda) which are not in V is a stationary subset of P_kappa(lambda). We consider problems of generalizing some work of Gitik, who showed that a new real makes the ground model globally co-stationary. For instance, what if the larger model has no new reals but does have a new countble-length sequences of ordinals? Or what if the larger model has no new countable-length sequences, but does have a new subset of aleph_1? We give answers to these questions, and pose many more.