{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:10Z","timestamp":1747150510568,"version":"3.40.5"},"reference-count":11,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"content-version":"vor","delay-in-days":11,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100008997","name":"University of Victoria","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008997","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*\u2010algebras that admit quantifier elimination in continuous logic are , , , and the continuous functions on the Cantor set. We show that, among finite dimensional C*\u2010algebras, 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 elements. Both of these predicates are definable, but not quantifier\u2010free definable, in the usual language of C*\u2010algebras. We also show that adding just the predicate for minimal projections is sufficient in the case of full matrix algebras, but that in general both new predicate symbols are\u00a0required.<\/jats:p>","DOI":"10.1002\/malq.201900041","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T11:03:09Z","timestamp":1576148589000},"page":"490-497","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Concrete barriers to quantifier elimination in finite dimensional C*\u2010algebras"],"prefix":"10.1002","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5428-7364","authenticated-orcid":false,"given":"Christopher J.","family":"Eagle","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics University of Victoria  P.O. Box 1700 STN CSC Victoria B.C., V8W 2Y2 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Todd","family":"Schmid","sequence":"additional","affiliation":[{"name":"Department of Computer Science University College London  Gower Street London WC1E 6BT United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,12]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735219.011"},{"key":"e_1_2_7_3_1","first-page":"347","article-title":"Nonnuclear subalgebras of C*\u2010algebras","volume":"14","author":"Blackadar B.","year":"1985","journal-title":"J. Operator Theory"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0360-9"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-07407-4_17"},{"volume-title":"C*\u2010Algebras by Example, Fields Institute Monographs","year":"1996","author":"Davidson K. R.","key":"e_1_2_7_6_1"},{"issue":"24","key":"e_1_2_7_7_1","first-page":"7580","article-title":"Quantifier elimination in C*\u2010algebras","volume":"2017","author":"Eagle C. J.","year":"2017","journal-title":"Int. Math. Res. Not."},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2016.04.008"},{"key":"e_1_2_7_9_1","unstructured":"I.Farah B.Hart M.Lupini L.Robert A.Tikuisis A.Vignati andW.Winter Model theory of C*\u2010algebras preprint (2018) arXiv:1602.08072v6."},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-014-1046-7"},{"key":"e_1_2_7_11_1","unstructured":"I.KlepandM.Tressl A model theoretic perspective of matrix rings preprint (2018) arXiv:1810.09024v2."},{"key":"e_1_2_7_12_1","doi-asserted-by":"crossref","DOI":"10.1525\/9780520348097","volume-title":"A Decision Method for Elementary Algebra and Geometry, Project Rand R\u2010109","author":"Tarski A.","year":"1951"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201900041","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900041","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201900041","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T22:12:28Z","timestamp":1694124748000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201900041"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1002\/malq.201900041"],"URL":"https:\/\/doi.org\/10.1002\/malq.201900041","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2019,12]]},"assertion":[{"value":"2019-06-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}