We will discuss our recent partial answer to a question of Hrušák: if a product of filters on ω is countable dense homogeneous, then the number of factors is smaller than p and each factor is a non-meager P-filter. Furthermore, we will show that non-meager P-filters can be characterized as the “chunkiest” filters with respect to Miller-measurability. As a rather “quotable” corollary, we will see that the intersection of fewer that add(m⁰) non-meager P-filters is a non-meager P-filter, where m⁰ denotes the ideal of Miller-null sets. All of these results build on an old joint paper with Kunen and Zdomskyy.

https://arxiv.org/abs/2601.17780