{"paper":{"title":"Logic and $\\mathrm{C}^*$-algebras: set theoretical dichotomies in the theory of continuous quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.OA"],"primary_cat":"math.LO","authors_text":"Alessandro Vignati","submitted_at":"2017-06-20T12:45:36Z","abstract_excerpt":"Given a nonunital $\\mathrm{C}^*$-algebra $A$ one constructs its corona algebra $\\mathcal M(A)/A$. This is the noncommutative analog of the \\v{C}ech-Stone remainder of a topological space. We analyze the two faces of these algebras: the first one is given assuming CH, and the other one arises when Forcing Axioms are assumed. In their first face, corona $\\mathrm{C}^*$-algebras have a large group of automorphisms that includes nondefinable ones. The second face is the Forcing Axiom one; here the automorphism group of a corona $\\mathrm{C}^*$-algebra is as rigid as possible, including only definabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06393","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"}