# Mutual Stationarity and Prikry-type forcings

Set theory seminarFriday, October 24, 201412:00 pmGC 6417

# Mutual Stationarity and Prikry-type forcings

### University of California, Berkeley

Mutual stationarity is a property first introduced by Foreman and Magidor to study saturation properties of nonstationary ideals. Given a sequence $\langle\kappa_i : i < \lambda\rangle$ of regular cardinals, a sequence $\langle S_i: i < \lambda\rangle$ with $S_i \subseteq \kappa_i$ stationary for every $i$, is mutually stationary iff there are stationarily many subsets $A \subseteq \sup_{i < \lambda} \kappa_i$ s.t. $\sup(A \cap \kappa_i) \in S_i$ for all $i$ with $\kappa_i \in A$. Consider this second property of a sequence $\langle\kappa_i : i < \lambda\rangle$: there is a forcing $P$ that changes $\text{cof}(\kappa_i)$ to $\eta_i$ without changing cofinalities or cardinalites of ordinals below $\inf{\kappa_i : i < \lambda}$. We want to discuss how, and why, these properties are related.

Dr. Dominik Adolf is currently a postdoctoral fellow at the University of California, Berkeley. He holds a PhD from the University of Münster, completed under the supervision of Ralf Schindler. His research interests include set theory, inner model theory, precipitous ideals, and stationary sets.

Posted by on October 17th, 2014