Place: Bahen Centre Information T . BA 2165
Date: May 11, 2018 (13:3015:00)
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.
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