{"paper":{"title":"Universal flows and automorphisms of $\\mathcal P(\\omega)/\\mathrm{fin}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.LO"],"primary_cat":"math.GN","authors_text":"Will Brian","submitted_at":"2018-02-06T16:39:05Z","abstract_excerpt":"We prove that for every countable discrete group $G$, there is a $G$-flow on $\\omega^*$ that has every $G$-flow of weight $\\leq\\! \\aleph_1$ as a quotient. It follows that, under the Continuum Hypothesis, there is a universal $G$-flow of weight $\\leq\\!\\mathfrak{c}$.\n  Applying Stone duality, we deduce that, under \\mathsf{CH}, there is a trivial automorphism $\\tau$ of $\\mathcal P(\\omega)/\\mathrm{fin}$ with every other automorphism embedded in it, which means that every other automorphism of $\\mathcal P(\\omega)/\\mathrm{fin}$ can be written as the restriction of $\\tau$ to a suitably chosen subalge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02055","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"}