{"paper":{"title":"Model-theoretic aspects of the Gurarij operator system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.LO","authors_text":"Isaac Goldbring, Martino Lupini","submitted_at":"2015-01-18T18:19:35Z","abstract_excerpt":"We establish some of the basic model theoretic facts about the Gurarij operator system $\\mathbb{GS}$ recently constructed by the second-named author. In particular, we show: (1) $\\mathbb{GS}$ is the unique separable 1-exact existentially closed operator system; (2) $\\mathbb{GS}$ is the unique separable nuclear model of its theory; (3) every embedding of $\\mathbb{GS}$ into its ultrapower is elementary; (4) $\\mathbb{GS}$ is the prime model of its theory; and (5) $\\mathbb{GS}$ does not have quantifier-elimination, whence the theory of operator systems does not have a model companion. We also show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04332","kind":"arxiv","version":3},"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"}