{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:17:49Z","timestamp":1775470669226,"version":"3.50.1"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":192,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this note, we show that the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of any locally universal, McDuff II<jats:sub>1<\/jats:sub> factor does not have quantifier elimination. We also show how a positive solution to the Connes Embedding Problem implies that there can be no model-complete theory of II<jats:sub>1<\/jats:sub> factors.<\/jats:p>","DOI":"10.2178\/jsl.7803170","type":"journal-article","created":{"date-parts":[[2014,1,6]],"date-time":"2014-01-06T13:18:22Z","timestamp":1389014302000},"page":"1000-1004","source":"Crossref","is-referenced-by-count":14,"title":["The Theory of Tracial Von Neumann Algebras Does Not Have A Model Companion"],"prefix":"10.1017","volume":"78","author":[{"given":"Isaac","family":"Goldbring","sequence":"first","affiliation":[]},{"given":"Bradd","family":"Hart","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Sinclair","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200126726_ref008","unstructured":"[8] Farah I. , Model theory of operator algebras II: Model theory, preprint."},{"key":"S0022481200126726_ref002","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1995.171.309"},{"key":"S0022481200126726_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-006-0074-y"},{"key":"S0022481200126726_ref001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061309000811"},{"key":"S0022481200126726_ref009","unstructured":"[9] Farah I. , Model theory of operator algebras III. Elementary equivalence and II1 factors, preprint."},{"key":"S0022481200126726_ref007","volume-title":"The Bulletin of the London Mathematical Society","author":"Farah"},{"key":"S0022481200126726_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdm054"},{"key":"S0022481200126726_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.04.003"},{"key":"S0022481200126726_ref006","volume-title":"C*-algebras and finite-dimensional approximations","volume":"88","author":"Brown","year":"2008"},{"key":"S0022481200126726_ref003","unstructured":"[3] Ben Yaacov I. , Henson C. W. , Junge M. , and Raynaud Y. , Report on non-commutative probabilities and von neumann algebras, http:\/\/www.aimath.org\/WWN\/continuouslogic\/ncpreport.pdf."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200126726","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T15:56:42Z","timestamp":1556035002000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200126726\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S0022481200126726"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7803170","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}