{"paper":{"title":"Seven characterizations of non-meager P-filters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Andrea Medini, Kenneth Kunen, Lyubomyr Zdomskyy","submitted_at":"2013-11-07T13:35:30Z","abstract_excerpt":"We give several topological/combinatorial conditions that, for a filter on $\\omega$, are equivalent to being a non-meager $\\mathsf{P}$-filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager $\\mathsf{P}$-filter. Here, we identify a filter with a subspace of $2^\\omega$ through characteristic functions. Along the way, we generalize to non-meager $\\mathsf{P}$-filters a result of Miller about $\\mathsf{P}$-points, and we employ and give a new proof of results of Marciszewski. We also employ a theorem of Hern\\'andez-Guti\\'errez and Hru\\v{s}\\'ak, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1677","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}