Ernest Schimmerling

### Mathematical logic seminar - October 16, 2002

 Speaker: John Krueger Graduate Student Department of Mathematical Sciences Carnegie Mellon University Title: Destroying stationary sets, part II Abstract:

I will discuss a new forcing technique which I developed for destroying the stationarity of subsets of

$P_\kappa \kappa^+ = \{ a \subseteq \kappa^+ : |a| < \kappa \}$
where $\kappa$ is weakly inaccessible. In order to destroy one stationary set while preserving the stationarity of another, it is necessary to "prepare" the ground model with a forcing iteration. However since the posets are not closed, the usual Easton support iteration does not work. Instead we use Gitik's Easton support Prikry iteration. I will describe these techniques and some of the problems which I solved using them.