# Osvaldo Guzman: hm and the ultrafilter number

Place: Bahen Centre Information T .   BA 2165
Date: May 11, 2018 (13:30-15:00)
Speaker: Osvaldo Guzman
Title: hm and the ultrafilter number
Abstract: The cardinal invariant $\mathfrak{hm}$ is defined as the minimum size of a family of $\mathsf{c}_{\mathsf{min}}$-monochromatic sets that cover $2^{\omega}$ (where $\mathsf{c}_{\mathsf{min}}\left( x,y\right)$ is the parity of the biggest initial segment both $x$ and $y$ have in common). We prove that $\mathfrak{hm}=\omega_{1}$ holds in the Shelah’s model of $\mathfrak{i<u}$ so the inequality $\mathfrak{hm<u}$ is consistent with the axioms of $\mathsf{ZFC.}$ This answers a question of Thilo Weinert.