{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T15:46:58Z","timestamp":1762271218102},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2293,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic><jats:bold>M<\/jats:bold><\/jats:italic> = \u3008<jats:italic>M<\/jats:italic>, +, &lt;, 0, {\u03bb}<jats:sub>\u03bb\u0404<jats:italic>D<\/jats:italic><\/jats:sub>\u3009 be an ordered vector space over an ordered division ring <jats:italic>D<\/jats:italic>, and <jats:italic>G<\/jats:italic> = \u3008<jats:italic>G<\/jats:italic>, \u2295, <jats:italic>e<jats:sub>G<\/jats:sub><\/jats:italic>\u3009 an <jats:italic>n<\/jats:italic>-dimensional group definable in <jats:italic><jats:bold>M<\/jats:bold><\/jats:italic>. We show that if <jats:italic>G<\/jats:italic> is definably compact and definably connected with respect to the <jats:italic>t<\/jats:italic>-topology, then it is definably isomorphic to a \u2018definable quotient group\u2019 <jats:italic>U\/L<\/jats:italic>, for some convex <jats:italic>V<\/jats:italic>-definable subgroup <jats:italic>U<\/jats:italic> of \u3008<jats:italic>M<jats:sup>n<\/jats:sup><\/jats:italic>, +\u3009 and a lattice <jats:italic>L<\/jats:italic> of rank <jats:italic>n<\/jats:italic>. As two consequences, we derive Pillay's conjecture for a saturated <jats:italic><jats:bold>M<\/jats:bold><\/jats:italic> as above and we show that the o-minimal fundamental group of <jats:italic>G<\/jats:italic> is isomorphic to <jats:italic>L<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1203350776","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T18:42:11Z","timestamp":1206470531000},"page":"1108-1140","source":"Crossref","is-referenced-by-count":20,"title":["Groups definable in ordered vector spaces over ordered division rings"],"prefix":"10.1017","volume":"72","author":[{"given":"Pantelis E.","family":"Eleftheriou","sequence":"first","affiliation":[]},{"given":"Sergei","family":"Starchenko","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200004813_ref021","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061304000346"},{"key":"S0022481200004813_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(88)90125-9"},{"key":"S0022481200004813_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(00)00027-0"},{"key":"S0022481200004813_ref002","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610701003015"},{"key":"S0022481200004813_ref007","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1215\/ijm\/1258138308","article-title":"Covers of groups definable in o-minimal structures","volume":"49","author":"Edmundo","year":"2005","journal-title":"Illinois Journal of Mathematics"},{"key":"S0022481200004813_ref022","volume-title":"Topological groups","author":"Pontrjagin","year":"1939"},{"key":"S0022481200004813_ref016","unstructured":"Onshuus A. , Groups definable in \u3008\u211a, +, <\u3009, preprint, 2005."},{"key":"S0022481200004813_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761295"},{"key":"S0022481200004813_ref013","volume-title":"Piecewise linear topology","author":"Hudson","year":"1969"},{"key":"S0022481200004813_ref009","unstructured":"Edmundo M. and Eleftheriou P. , The universal covering homomorphism in o-minimal expansions of groups, preprint, 10 2006."},{"key":"S0022481200004813_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.01.002"},{"key":"S0022481200004813_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12918-0"},{"key":"S0022481200004813_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(03)00085-9"},{"key":"S0022481200004813_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.04.016"},{"key":"S0022481200004813_ref010","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061304000358"},{"key":"S0022481200004813_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525919"},{"key":"S0022481200004813_ref011","volume-title":"Agebraic topology","author":"Hatcher","year":"2002"},{"key":"S0022481200004813_ref012","article-title":"Groups, measures, and the NIP","author":"Hrushovski","journal-title":"Journal of the American Mathematical Society"},{"key":"S0022481200004813_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0041-0"},{"key":"S0022481200004813_ref023","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(94)90127-9"},{"key":"S0022481200004813_ref017","volume-title":"Manuscripta Mathematicae","author":"Peterzil"},{"key":"S0022481200004813_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00016-0"},{"key":"S0022481200004813_ref019","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799007528"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200004813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T19:42:36Z","timestamp":1556739756000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200004813\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["S0022481200004813"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1203350776","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}