{"paper":{"title":"On some relations between properties of invariant $\\sigma$-ideals in Polish spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Marcin Michalski","submitted_at":"2019-07-18T22:37:16Z","abstract_excerpt":"In this paper we shall consider a couple of properties of $\\sigma$-ideals and study relations between them. Namely we will prove that $\\mathfrak{c}$-cc $\\sigma$-ideals are tall and that the Weaker Smital Property implies that every Borel $\\mathcal{I}$-positive set contains a witness for non($\\mathcal{I}$) as well, as satisfying ccc and Fubini Property. We give also a characterization of nonmeasurability of $\\mathcal{I}$-Luzin sets and prove that the ideal $[\\mathbb{R}]^{\\leq\\omega}$ does not posses the Fubini Property using some interesting lemma about perfect sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09306","kind":"arxiv","version":1},"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"}