Louise Hay Logic Seminar
Noah Schoem
Mutual Stationarity
Abstract: 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.
Wednesday December 4, 2019 at 4:00 PM in 427 SEO