Global Square and Mutual Stationarity at the Aleph_n

TL;DR

This paper demonstrates that the mutual stationarity property for sequences of stationary sets at Aleph_n implies the existence of inner models with high Mitchell order measurables, using the Global Square property in core models.

Contribution

It establishes a link between mutual stationarity at Aleph_n and the existence of inner models with high Mitchell order measurables, extending previous results.

Findings

Mutual stationarity at Aleph_n implies inner models with high Mitchell order measurables.

Uses the Global Square property in core models below a measurable of Mitchell order.

Connects stationary set properties with inner model existence.

Abstract

We show using a proof of the Global Square property in Core Models below a measurable of Mitchell order o(kappa)=kappa^++ (a result originally due to Jensen & Zeman) that Foreman and Magidor's Mutual Stationarity property MS(Aleph_n (1<n<omega), Cof(omega_1)) implies the existence of inner models with measurables of high Mitchell order. This MS property states that any sequence of independently chosen stationary subsets S_n of the Aleph_n (of fixed cofinality omega_1) is mutually stationary below aleph_omega.