{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:18:35Z","timestamp":1754108315925},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","funder":[{"name":"Independent Research","award":["MTM2017-82105"],"award-info":[{"award-number":["MTM2017-82105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. (N.S.) 18(4) (2012) 885\u2013903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061320500099","type":"journal-article","created":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T08:30:16Z","timestamp":1570437016000},"page":"2050009","source":"Crossref","is-referenced-by-count":2,"title":["Locally definable subgroups of semialgebraic groups"],"prefix":"10.1142","volume":"20","author":[{"given":"El\u00edas","family":"Baro","sequence":"first","affiliation":[{"name":"Departamento de \u00c1lgebra, Geometr\u00eda y Topolog\u00eda, Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pantelis E.","family":"Eleftheriou","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Konstanz, Box 216, 78457 Konstanz, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya\u2019acov","family":"Peterzil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Haifa, Haifa, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"S0219061320500099BIB001","doi-asserted-by":"publisher","DOI":"10.2307\/1970178"},{"key":"S0219061320500099BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.03.003"},{"key":"S0219061320500099BIB004","first-page":"1","author":"Berarducci A.","year":"2012","journal-title":"Selecta Math."},{"key":"S0219061320500099BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-06307-1"},{"key":"S0219061320500099BIB006","volume-title":"A Brief Introduction to Approximate Groups","volume":"61","author":"Breuillard E.","year":"2013"},{"key":"S0219061320500099BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758635"},{"key":"S0219061320500099BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.04.016"},{"key":"S0219061320500099BIB009","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610051"},{"key":"S0219061320500099BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00029-012-0091-5"},{"key":"S0219061320500099BIB011","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2143889"},{"key":"S0219061320500099BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2011-00708-X"},{"key":"S0219061320500099BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758643"},{"key":"S0219061320500099BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-07-00558-9"},{"key":"S0219061320500099BIB015","doi-asserted-by":"crossref","first-page":"5","DOI":"10.5802\/jep.17","volume":"2","author":"Massicot J. 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