{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:28:32Z","timestamp":1772447312826,"version":"3.50.1"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1380,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems:<\/jats:p><jats:p>1. when the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the <jats:italic>co-strongly minimal<\/jats:italic> case);<\/jats:p><jats:p>2. when the theory of the structure is strongly minimal.<\/jats:p><jats:p>In the first case, we identify the abelian structure as a \u201cnear-subspace\u201d <jats:italic>A<\/jats:italic> of a vector space <jats:italic>V<\/jats:italic> over a division ring <jats:italic>D<\/jats:italic> with its induced structure, with possibly some collection of distinguished subgroups of <jats:italic>A<\/jats:italic> of finite index in <jats:italic>A<\/jats:italic> and (up to <jats:italic>acl<\/jats:italic>(\u2205)) no further structure. In the second, the structure is that of <jats:italic>V\/A<\/jats:italic> for a vector space and near-subspace as above, with the only further possible structure some collection of distinguished points. Here a near-subspace of <jats:italic>V<\/jats:italic> is a subgroup <jats:italic>A<\/jats:italic> such that for any nonzero <jats:italic>d<\/jats:italic> \u2208 <jats:italic>D<\/jats:italic>. the index of <jats:italic>A<\/jats:italic> \u2229 <jats:italic>dA<\/jats:italic>, in <jats:italic>A<\/jats:italic> is finite. We also show that any weakly minimal abelian structure is a reduct of a weakly minimal module.<\/jats:p>","DOI":"10.2178\/jsl\/1268917489","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"442-458","source":"Crossref","is-referenced-by-count":2,"title":["Strongly and co-strongly minimal abelian structures"],"prefix":"10.1017","volume":"75","author":[{"given":"Ehud","family":"Hrushovski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Loveys","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002620_ref009","first-page":"339","volume":"48","author":"Poizat","year":"1983","journal-title":"Groupes stables, avec types g\u00e9n\u00e9riques r\u00e9guliers"},{"key":"S0022481200002620_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(84)90014-9"},{"key":"S0022481200002620_ref003","first-page":"1184","volume":"56","author":"Buechler","year":"1991","journal-title":"Pseudo-projective strongly minimal sets are projective"},{"key":"S0022481200002620_ref002","first-page":"1044","volume":"50","author":"Buechler","year":"1985","journal-title":"The geometry of weakly minimal types"},{"key":"S0022481200002620_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082236"},{"key":"S0022481200002620_ref004","first-page":"670","volume":"55","author":"Gute","year":"1990","journal-title":"The last word on quantifier elimination in modules"},{"key":"S0022481200002620_ref010","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600562"},{"key":"S0022481200002620_ref006","volume-title":"Logic Colloquium '85","author":"Hrushovski","year":"1986"},{"key":"S0022481200002620_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(79)90230-8"},{"key":"S0022481200002620_ref007","first-page":"928","volume":"55","author":"Loveys","year":"1990","journal-title":"Weakly minimal groups of unbounded exponent"},{"key":"S0022481200002620_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01375550"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002620","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T19:37:46Z","timestamp":1556480266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002620\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["S0022481200002620"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1268917489","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}