Rudin-Keisler capturing and Mutual Stationairy at successors of Singulars

TL;DR

This paper introduces a new combinatorial measure called Rudin-Keisler capturing to construct elementary substructures around singular cardinals, leading to mutual stationary results at their first successors.

Contribution

It presents a novel combinatorial notion and applies it to establish mutual stationary properties at successors of singular cardinals.

Findings

Established mutual stationary results at the first successor of singulars.

Developed a new construction of elementary substructures using Rudin-Keisler capturing.

Introduced a combinatorial measure for analyzing singular cardinals.

Abstract

We introduce a combinatorial notion of measures called Rudin-Keisler capturing and use it to give a new construction of elementary substructures around singular cardinals. The new construction is used to establish mutual stationary results at the first successor of singular cardinals $\langle \aleph_{\omega n + 1}\rangle_{n< \omega}$.