# Ultrafilters on singular cardinals of uncountable cofinality

## TL;DR

This paper demonstrates the consistent existence of a singular uncountable cofinality cardinal with a weakly inaccessible power set, where all intermediate regular cardinals are ultrafilter characters, advancing set theory understanding.

## Contribution

It establishes the consistent existence of such a cardinal with specific ultrafilter and cardinal properties, linking ultrafilter characters to large cardinal hypotheses.

## Key findings

- Existence of a singular cardinal with uncountable cofinality and a weakly inaccessible power set.
- All regular cardinals between the singular and its power set are ultrafilter characters.
- Provides a new consistency result connecting ultrafilters and large cardinals.

## Abstract

We prove that consistently there is a singular cardinal $\kappa$ of uncountable cofinality such that $2^\kappa$ is weakly inaccessible, and every regular cardinal strictly between $\kappa$ and $2^\kappa$ is the character of some uniform ultrafilter on $\kappa$.