Noah Schoem : Mutual Stationarity

Posted by Noah Schoem , part of the Louise Hay Logic Seminar.

At

Dec. 4, 2019, 4 p.m.

In

427 SEO

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.