An almost strong relation

Abstract

Let $\mu$ be a strong limit singular cardinal. We prove that if $2^{\mu }>{\mu }^{+}$ then $\left(\genfrac{}{}{0ex}{}{{\mu }^{+}}{\mu }\right)\to {\left(\genfrac{}{}{0ex}{}{\tau }{\mu }\right)}_{<\mathrm{cf}(\mu )}$ for every ordinal $\tau <{\mu }^{+}$. We obtain an optimal positive relation under $2^{\mu }={\mu }^{+}$, as after collapsing $2^{\mu }$ to ${\mu }^{+}$ this positive relation is preserved.

Accepted for publication by the Bulletin of the Belgian Mathematical Society - October 2023

References in corpus (3)

• A strong polarized relation
• Open and solved problems concerning polarized partition relations
• Unbalanced polarized relations