# Cardinal characteristics at aleph omega

## TL;DR

This paper establishes the consistency of a specific inequality involving cardinal characteristics at leph_omega, linking it to the existence of a measurable cardinal with a particular order.

## Contribution

It proves the exact consistency strength of the inequality rak{u}_{\u001domega}<2^{omega} as a measurable cardinal with order omega^{++}.

## Key findings

- Consistency of rak{u}_{omega}<2^{omega} established.
- Exact consistency strength identified as a measurable cardinal with order omega^{++}.
- Links between cardinal characteristics and large cardinal assumptions clarified.

## Abstract

We prove the consistency of the statement $\mathfrak{u}_{\aleph_\omega}<2^{\aleph_\omega}$. We show that the consistency strength of this statement is exactly a measurable cardinal $\mu$ so that $o(\mu)=\mu^{++}$.