Infinite Monochromatic Paths and a Theorem of Erdős-Hajnal-Rado
Abstract
We prove that if $\mu$ is a singular cardinal with countable cofinality and $2^\mu=\mu^+$ then $\binom{\mu^+}{\mu}\nrightarrow\binom{\mu^+\ \aleph_2}{\mu\ \mu}$.
We prove that if $\mu$ is a singular cardinal with countable cofinality and $2^\mu=\mu^+$ then $\binom{\mu^+}{\mu}\nrightarrow\binom{\mu^+\ \aleph_2}{\mu\ \mu}$.