# Partitioning a reflecting stationary set

## TL;DR

This paper investigates the partitioning of reflecting stationary sets into multiple subsets within ZFC, and explores implications for singular cardinals, showing certain configurations are impossible.

## Contribution

It provides new results affirming the partitionability of reflecting stationary sets in ZFC and applies these findings to singular cardinal combinatorics.

## Key findings

- Reflecting stationary sets can be partitioned into multiple reflecting subsets in ZFC.
- It is impossible for a singular cardinal to have all scales being very good.

## Abstract

We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is never the case that there exists a singular cardinal all of whose scales are very good.