{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T14:05:31Z","timestamp":1649081131379},"reference-count":14,"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":3388,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>In a simple theory with elimination of finitary hyperimaginaries if tp(<jats:italic>a<\/jats:italic>) is real and analysable over a definable set <jats:italic>Q<\/jats:italic>, then there exists a finite sequence (<jats:italic>a<jats:sub>i<\/jats:sub><\/jats:italic> \\ <jats:italic>i<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>*) \u2286 dcl<jats:sup><jats:italic>eq<\/jats:italic><\/jats:sup>(<jats:italic>a<\/jats:italic>) with <jats:italic>a<jats:sub>n*<\/jats:sub><\/jats:italic> = <jats:italic>a<\/jats:italic> such that for every <jats:italic>i<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>* if <jats:italic>p<jats:sub>i<\/jats:sub><\/jats:italic> = tp(<jats:italic>a<jats:sub>i<\/jats:sub><\/jats:italic>\/{<jats:italic>a<jats:sub>j<\/jats:sub><\/jats:italic> |<jats:italic>j<\/jats:italic> &lt; <jats:italic>i<\/jats:italic>}) then Aut(<jats:italic>p<jats:sub>i<\/jats:sub><\/jats:italic> \/ <jats:italic>Q<\/jats:italic>) is type-definable with its action on <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200007489_inline1\" \/>. A unidimensional simple theory eliminates the quantifier \u2203<jats:sup>\u221e<\/jats:sup> and either interprets (in <jats:italic>C<jats:sup>eq<\/jats:sup><\/jats:italic>) an infinite type-definable group or has the property that ACL(<jats:italic>Q<\/jats:italic>) = <jats:italic>C<\/jats:italic> for every infinite definable set <jats:italic>Q<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1102022220","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:51:53Z","timestamp":1109800313000},"page":"1221-1242","source":"Crossref","is-referenced-by-count":4,"title":["Coordinatisation by binding groups and unidimensionality in simple theories"],"prefix":"10.1017","volume":"69","author":[{"given":"Ziv","family":"Shami","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007489_ref014","first-page":"359\u2013368","volume-title":"Proceedings of the international congress of mathematicians, vol. 1, 2 (Warsaw, 1983)","author":"Zilber","year":"1984"},{"key":"S0022481200007489_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3002-0"},{"key":"S0022481200007489_ref011","doi-asserted-by":"crossref","first-page":"177\u2013203","DOI":"10.1016\/0003-4843(80)90009-1","article-title":"Simple unstable theories","volume":"19","author":"Shelah","year":"1980","journal-title":"Annals of Mathematical Logic"},{"key":"S0022481200007489_ref010","first-page":"1016\u20131024","volume":"67","author":"Shami","year":"2002","journal-title":"On the binding group in simple theories"},{"key":"S0022481200007489_ref009","doi-asserted-by":"crossref","first-page":"149\u2013162","DOI":"10.1016\/j.apal.2003.12.004","article-title":"Internality and interpretable automorphism groups in simple theories","volume":"129","author":"Shami","year":"2004","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481200007489_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00019-5"},{"key":"S0022481200007489_ref006","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610798005985"},{"key":"S0022481200007489_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-00-00350-7"},{"key":"S0022481200007489_ref005","first-page":"97\u2013138","volume-title":"Differential galois theory","volume":"58","author":"Hrushovski","year":"2002"},{"key":"S0022481200007489_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90046-5"},{"key":"S0022481200007489_ref013","unstructured":"Wagner Frank O. , On almost orthogonality in simple theories, preprint."},{"key":"S0022481200007489_ref002","first-page":"293\u2013309","volume":"65","author":"Hart","year":"2000","journal-title":"Coordinatisation and canonical bases in simple theories"},{"key":"S0022481200007489_ref008","unstructured":"Newelski L. , The diameter of a Lascar strong type, preprint."},{"key":"S0022481200007489_ref003","unstructured":"Hart B. and Shami Z. , On the type-definability of the binding group in simple theories, this Journal, to appear."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007489","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T19:38:42Z","timestamp":1557171522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007489\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,12]]}},"alternative-id":["S0022481200007489"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1102022220","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}