{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:27:54Z","timestamp":1772447274240,"version":"3.50.1"},"reference-count":14,"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":4940,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A structure (<jats:italic>M<\/jats:italic>, &lt;, \u2026) is called <jats:italic>quasi-o-minimal<\/jats:italic> if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of <jats:italic>U<\/jats:italic>-rank 1.<\/jats:p>","DOI":"10.2307\/2586690","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:41Z","timestamp":1146938561000},"page":"1115-1132","source":"Crossref","is-referenced-by-count":29,"title":["Quasi-o-minimal structures"],"prefix":"10.1017","volume":"65","author":[{"given":"Oleg","family":"Belegradek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya'acov","family":"Peterzil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011816_ref002","first-page":"21\u201332","volume-title":"Logical Foundations of Computer Science (Proceedings 4th International Symposium LFCS'97, Yaroslavl, Russia, July 1997)","author":"Belegradek","year":"1997"},{"key":"S0022481200011816_ref011","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1990"},{"key":"S0022481200011816_ref003","first-page":"64\u201388","volume-title":"Proceedings of the 3rd Easter Conference on Model Theory (Gro\u00df K\u00f6ris, April 8\u201313, 1985)","author":"Dickmann","year":"1985"},{"key":"S0022481200011816_ref006","first-page":"817\u2013831","volume":"60","author":"Laskowski","year":"1995","journal-title":"On o-minimal expansions of archimedian ordered groups"},{"key":"S0022481200011816_ref013","first-page":"131\u2013155","volume-title":"Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de Belgique","author":"Weispfenning","year":"1981"},{"key":"S0022481200011816_ref001","first-page":"1998","volume-title":"MSRI preprint series","author":"Belegradek"},{"key":"S0022481200011816_ref014","first-page":"21\u201340","volume-title":"Transactions of the Amererican Mathematical Society","author":"Zakon","year":"1961"},{"key":"S0022481200011816_ref004","volume-title":"The Schur multipliers","volume":"2","author":"Karpilovski","year":"1987"},{"key":"S0022481200011816_ref005","first-page":"565\u2013592","volume-title":"Transactions of the American Mathematical Society","author":"Knight","year":"1986"},{"key":"S0022481200011816_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00022-4"},{"key":"S0022481200011816_ref008","volume-title":"An introduction to stability theory","author":"Pillay","year":"1983"},{"key":"S0022481200011816_ref010","first-page":"469\u2013476","volume-title":"Transactions of the American Mathematical Society","author":"Pillay","year":"1988"},{"key":"S0022481200011816_ref012","first-page":"133\u2013185","volume-title":"Logic: from Foundations to Applications (European Logic Colloquium'93)","author":"van den Dries","year":"1996"},{"key":"S0022481200011816_ref009","first-page":"593\u2013605","volume-title":"Transactions of the American Mathematical Society","author":"Pillay","year":"1986"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011816","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T20:47:04Z","timestamp":1557348424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011816\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S0022481200011816"],"URL":"https:\/\/doi.org\/10.2307\/2586690","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}