# Infinite monochromatic paths and a theorem of Erdos-Hajnal-Rado

## TL;DR

The paper proves a specific partition relation failure for infinite monochromatic paths under certain set-theoretic assumptions involving cardinals and continuum hypotheses.

## Contribution

It establishes a new negative partition relation result for infinite monochromatic paths in a particular set-theoretic context.

## Key findings

- Shows that under certain conditions, a strong partition relation does not hold.
- Provides a counterexample to a potential generalization of the Erdős-Hajnal-Rado theorem.
- Advances understanding of combinatorial properties of infinite cardinals.

## Abstract

We prove that if $\mu>{\rm cf}(\mu)=\omega$ and $2^\mu=\mu^+$ then $\binom{\mu^+}{\mu}\nrightarrow\binom{\mu^+\ \aleph_2}{\mu\ \mu}$.