{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T10:37:34Z","timestamp":1649068654640},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6585,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that there are 2<jats:sup><jats:italic>\u03c7<\/jats:italic>0<\/jats:sup> pairwise non elementarily equivalent existentially closed ordered groups, which solve the main open problem in this area (cf. [3, 10]).<\/jats:p><jats:p>A simple direct proof is given of the weaker fact that the theory of ordered groups has no model companion; the case of the ordered division rings over a field <jats:italic>k<\/jats:italic> is also investigated.<\/jats:p><jats:p>Our main result uses constructible sets and can be put in an abstract general framework.<\/jats:p><jats:p>Comparison with the standard methods which use forcing (cf. [4]) is sketched.<\/jats:p>","DOI":"10.2307\/2275610","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:57:36Z","timestamp":1146956256000},"page":"277-284","source":"Crossref","is-referenced-by-count":2,"title":["Existentially closed models via constructible sets: There are 2<sup><i>\u2135<\/i>0<\/sup> existentially closed pairwise non elementarily equivalent existentially closed ordered groups"],"prefix":"10.1017","volume":"61","author":[{"given":"Anatole","family":"Khelif","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120001776X_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1949-0032593-5"},{"key":"S002248120001776X_ref008","volume-title":"Lectures in pure and applied mathematics","volume":"27","author":"Mura","year":"1977"},{"key":"S002248120001776X_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1970894"},{"key":"S002248120001776X_ref002","volume-title":"Mathematics and its applications","author":"Glass","year":"1989"},{"key":"S002248120001776X_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02762049"},{"key":"S002248120001776X_ref006","volume-title":"Basic set theory","author":"Levy","year":"1978"},{"key":"S002248120001776X_ref001","article-title":"Elementary properties of algebraically closed groups","volume":"98","author":"Belegradek","year":"1978","journal-title":"Fundamenta Mathematicae"},{"key":"S002248120001776X_ref010","unstructured":"Simonetta P. , Th\u00e9se de doctorat: \u201cd\u00e9cidabilit\u00e9 et interpr\u00e9tabilit\u00e9 dans les corps et les groupes non commutatifs\u201d, Universit\u00e9 Paris VII, 1994."},{"key":"S002248120001776X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064082"},{"key":"S002248120001776X_ref011","volume-title":"Word problems II","author":"Ziegler","year":"1980"},{"key":"S002248120001776X_ref005","volume-title":"Encyclopedia of mathematics and its applications","volume":"42","author":"Hodges","year":"1993"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120001776X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T19:07:26Z","timestamp":1557774446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120001776X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S002248120001776X"],"URL":"https:\/\/doi.org\/10.2307\/2275610","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}