{"paper":{"title":"On critical cardinalities related to $Q$-sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Lubomyr Zdomskyy, Michal Machura, Taras Banakh","submitted_at":"2013-06-02T12:41:52Z","abstract_excerpt":"In this note we collect some known information and prove new results about the small uncountable cardinal $\\mathfrak q_0$. The cardinal $\\mathfrak q_0$ is defined as the smallest cardinality $|A|$ of a subset $A\\subset \\mathbb R$ which is not a $Q$-set (a subspace $A\\subset\\mathbb R$ is called a $Q$-set if each subset $B\\subset A$ is of type $F_\\sigma$ in $A$). We present a simple proof of a folklore fact that $\\mathfrak p\\le\\mathfrak q_0\\le\\min\\{\\mathfrak b,\\mathrm{non}(\\mathcal N),\\log(\\mathfrak c^+)\\}$, and also establish the consistency of a number of strict inequalities between the cardin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0204","kind":"arxiv","version":3},"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"}