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


   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.