Non-meager $\mathsf{P}$-filters, Miller-measurability, and a question of Hrušák

Andrea Medini

Given a cardinal $\hat{I}º$ and filters ${\mathcal{F}}_{\hat{I}}\pm$ on $\ddot{I}‰$ for $\hat{I}\pm \in \hat{I}º$, we will show that if ${\prod }_{\hat{I}\pm \in \hat{I}º}{\mathcal{F}}_{\hat{I}}\pm$ is countable dense homogeneous then $\hat{I}º<\mathfrak{p}$…