Splitting stationary sets from weak forms of Choice

TL;DR

This paper investigates the conditions under which stationary sets can be partitioned into many parts within models that assume weaker forms of the Axiom of Choice, extending previous work in the area.

Contribution

It advances understanding of stationary set splitting under restricted Choice, providing new results for regular cardinals and their cofinalities.

Findings

Established new splitting results for stationary sets under weak Choice assumptions

Extended previous work to broader classes of regular cardinals

Provided conditions for partitioning stationary sets into many parts

Abstract

Working in the context of restricted forms of the Axiom of Choice, we consider the problem of splitting the ordinals below $\lambda$ of cofinality $\theta$ into $\lambda$ many stationary sets, where $\theta < \lambda$ are regular cardinals. This is a continuation of \cite{Sh835}.