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

Andrea Medini

Given a cardinal $\kappa$ and filters ${\mathcal{F}}_{\alpha }$ on $\omega$ for $\alpha \in \kappa$, we will show that if ${\prod }_{\alpha \in \kappa }{\mathcal{F}}_{\alpha }$ is countable dense homogeneous then $\kappa <\mathfrak{p}$ and each…