2013/11/07 by Kenneth Kunen, Kunen, Kenneth, Andrea Medini +3 · 1 citation
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1311.1677
openalex publication_date 2013/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager P-filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager P-filter. Here, we identify a filter with a subspace of 2ω through characteristic functions. Along the way, we generalize to non-meager P-filters a result of Miller about P-points, and we employ and give a new proof of results of Marciszewski. We also employ a theorem of Hernández-Gutiérrez and Hrušák, and answer two questions that they posed. Our result also resolves several issues raised by Medini and Milovich, and proves false one "theorem" of theirs. Furthermore, we show that the statement "Every non-meager filter contains a non-meager P-subfilter" is independent of ZFC (more precisely, it is a consequence of \mathfraku