{"paper":{"title":"Quantifier elimination in C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.LO","authors_text":"Alessandro Vignati, Christopher J. Eagle, Eberhard Kirchberg, Ilijas Farah","submitted_at":"2015-02-02T18:39:41Z","abstract_excerpt":"The only C*-algebras that admit elimination of quantifiers in continuous logic are $\\mathbb{C}, \\mathbb{C}^2$, $C($Cantor space$)$ and $M_2(\\mathbb{C})$. We also prove that the theory of C*-algebras does not have model companion and show that the theory of $M_n(\\mathcal {O_{n+1}})$ is not $\\forall\\exists$-axiomatizable for any $n\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00573","kind":"arxiv","version":5},"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"}