{"paper":{"title":"Concrete Barriers to Quantifier Elimination in Finite-Dimensional C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.LO","authors_text":"Christopher J. Eagle, Todd Schmid","submitted_at":"2019-05-29T01:08:51Z","abstract_excerpt":"Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*-algebras that admit quantifier elimination in continuous logic are $\\mathbb{C},$ $\\mathbb{C}^2,$ $M_2(\\mathbb{C}),$ and the continuous functions on the Cantor set. We show that, among finite dimensional C*-algebras, quantifier elimination does hold if the language is expanded to include two new predicate symbols: One for minimal projections, and one for pairs of unitarily conjugate projections. Both of these predicates are definable, but not quantifier-free definable, in the usual language of C*-algebras. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12153","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"}