{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:48:45Z","timestamp":1773820125197,"version":"3.50.1"},"reference-count":8,"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":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the structure (C, +, \u00b7) has no proper non locally modular reducts which contain +. In other words, if <jats:italic>X<\/jats:italic> \u2282 C<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> is constructible and <jats:italic>not<\/jats:italic> definable in the module structure (C, +, <jats:italic>\u03bb<jats:sub>a<\/jats:sub><\/jats:italic>)<jats:sub><jats:italic>a<\/jats:italic> \u0404 <jats:italic>C<\/jats:italic><\/jats:sub> (where <jats:italic>\u03bb<jats:sub>a<\/jats:sub><\/jats:italic> denotes multiplication by <jats:italic>a<\/jats:italic>) then multiplication is definable in (<jats:italic>C<\/jats:italic>, +, <jats:italic>X<\/jats:italic>).<\/jats:p>","DOI":"10.2307\/2274485","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:36:50Z","timestamp":1146940610000},"page":"1243-1251","source":"Crossref","is-referenced-by-count":13,"title":["Reducts of (C, +, \u00b7) which contain +"],"prefix":"10.1017","volume":"55","author":[{"given":"D.","family":"Marker","sequence":"first","affiliation":[]},{"given":"A.","family":"Pillay","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025676_ref007","unstructured":"Zilber B. , Some remarks on the model theory of algebraically closed fields, preprint, 1989."},{"key":"S0022481200025676_ref006","volume-title":"Groupes stables","author":"Poizat","year":"1987"},{"key":"S0022481200025676_ref003","unstructured":"Hrushovski E. , Contributions to stable model theory, Ph. D. thesis, University of California, Berkeley, California, 1986."},{"key":"S0022481200025676_ref001","first-page":"199","volume-title":"The model theory of groups","author":"Bouscaren","year":"1989"},{"key":"S0022481200025676_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6313-5"},{"key":"S0022481200025676_ref008","unstructured":"Zilber B. and Rabinovitch E. , Additive reducts of algebraically closed fields, manuscript, 1988."},{"key":"S0022481200025676_ref005","first-page":"188","volume":"53","author":"Martin","year":"1988","journal-title":"Definability in reducts of algebraically closed fields"},{"key":"S0022481200025676_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70556-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025676","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:24:37Z","timestamp":1558196677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025676\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0022481200025676"],"URL":"https:\/\/doi.org\/10.2307\/2274485","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}