{"paper":{"title":"Free sequences in P({\\omega})/fin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Chodounsk\\'y, Jan Greb\\'ik, Vera Fischer","submitted_at":"2018-08-17T17:02:00Z","abstract_excerpt":"We investigate maximal free sequences in the Boolean algebra $\\mathcal{P}(\\omega)/\\mathrm{fin}$, as defined by D. Monk. We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted $\\mathfrak{f}$. Answering a question of Monk, we demonstrate the consistency of $\\omega_1 = \\mathfrak{i} = \\mathfrak{f} < \\mathfrak{u} = \\omega_2$. In fact, this consistency is demonstrated in the model of S. Shelah for $\\mathfrak{i} < \\mathfrak{u}$. Our paper provides a strea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05930","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"}