Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities

TL;DR

This paper establishes near-optimal upper bounds on the consistency strength of certain mutual stationarity properties with divergent uncountable cofinalities, advancing understanding in set theory.

Contribution

It provides new upper bounds for the consistency strength of mutual stationarity with divergent uncountable cofinalities, showing these bounds are close to optimal.

Findings

Upper bounds for mutual stationarity consistency strength are nearly optimal

Analysis of stronger related properties in set theory

Advances understanding of uncountable cofinalities in mutual stationarity

Abstract

We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also consider some related and, as it turns out, stronger properties.