On Singular Stationarity I (mutual stationarity and ideal-based methods)

TL;DR

This paper explores ideal-based methods and advanced set-theoretic techniques to establish consistency results about mutually stationary sets and stationary sequences on uncountable cardinals, addressing a question by Foreman and Magidor.

Contribution

It introduces new consistency results in singular stationarity using strong ideals, supercompact embeddings, and Prikry-type posets, advancing understanding of stationary sequences on $eth_n$.

Findings

Established three new consistency results for mutually stationary sets.

Answered a question of Foreman and Magidor on stationary sequences.

Combined methods of strong ideals, supercompact embeddings, and Prikry-type posets.

Abstract

We study several ideal-based constructions in the context of singular stationarity. By combining methods of strong ideals, supercompact embeddings, and Prikry-type posets, we obtain three consistency results concerning mutually stationary sets, and answer a question of Foreman and Magidor concerning stationary sequences on the first uncountable cardinals, $\aleph_n$, $1 \leq n < \omega$.