# Louise Hay Logic Seminar: Mutual Stationarity, by Noah Schoem

December 4, 2019

4:00 PM - 4:50 PM

Noah Schoem: Mutual Stationarity

We can say that a set $S\subseteq\kappa$ is stationary if for any $\lambda>\kappa$

and every model $\mathcal{U}=\langle H_\lambda,\in,\dots\rangle$

there is an $M\prec \mathcal{U}$ such that $\sup(M\cap\kappa)\in S$.

But what if we want this result for a sequence of stationary sets simultaneously,

that is, given $\langle S_\alpha\mid \alpha<\tau\rangle$, each
$S_\alpha$ stationary in some $\kappa_\alpha<\tau$,
for every $\mathcal{U}=\langle H_\lambda,\in,\dots\rangle$ with $\lambda<\kappa_\tau$,
is there an $M\prec \mathcal{U}$ such that for all $\alpha<\tau$, $\sup(M\cap \kappa_\alpha)\in S_\alpha$?
We will explore what originally motivated this question and consistency results surrounding mutual stationarity.
Please click here to make changes to, or delete, this seminar announcement.

## Date posted

Dec 13, 2019

## Date updated

Dec 13, 2019