{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:58:29Z","timestamp":1759147109670},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8046,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/> be a countable saturated structure, and assume that <jats:italic>D(v)<\/jats:italic> is a strongly minimal formula (without parameter) such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/> is the algebraic closure of <jats:italic>D<\/jats:italic>(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/>). We will prove the two following theorems:<\/jats:p><jats:p>Theorem 1. <jats:italic>If G is a subgroup of Aut(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/>) of countable index, there exists a finite set A in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/> such that every A-strong automorphism is in G<\/jats:italic>.<\/jats:p><jats:p>Theorem 2. <jats:italic>Assume that G is a normal subgroup of Aut(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/>) containing an element g such that for all n there exists X \u2286 D(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120002329X_inline1\" \/>) such that Dim(g(X)\/X) &gt; n. Then every strong automorphism is in G<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2275188","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:43:45Z","timestamp":1146955425000},"page":"238-251","source":"Crossref","is-referenced-by-count":7,"title":["Les automorphismes d'un ensemble fortement minimal"],"prefix":"10.1017","volume":"57","author":[{"given":"Daniel","family":"Lascar","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120002329X_ref012","volume-title":"Commutative algebra","volume":"1","author":"Zariski","year":"1958"},{"key":"S002248120002329X_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90212-3"},{"key":"S002248120002329X_ref009","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S002248120002329X_ref008","first-page":"426","article-title":"Endomorphisms of infinite symmetric groups","volume":"2","author":"Semmes","year":"1981","journal-title":"Abstracts of Papers Presented to the American Mathematical Society"},{"key":"S002248120002329X_ref007","volume-title":"Cours de th\u00e9orie des mod\u00e9les","author":"Poizat","year":"1985"},{"key":"S002248120002329X_ref006","volume-title":"Archiv der Mathematik","author":"Lascar"},{"key":"S002248120002329X_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-62.1.25"},{"key":"S002248120002329X_ref004","volume-title":"Topology","volume":"1","author":"Kuratowski","year":"1966"},{"key":"S002248120002329X_ref001","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/18.6.580"},{"key":"S002248120002329X_ref002","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/18.6.587"},{"key":"S002248120002329X_ref003","first-page":"53","volume-title":"Logic Colloquium '87","author":"Hodges","year":"1989"},{"key":"S002248120002329X_ref011","volume-title":"Generic automorphisms of homogeneous structures","author":"Truss","year":"1990"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120002329X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T22:32:57Z","timestamp":1558045977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120002329X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["S002248120002329X"],"URL":"https:\/\/doi.org\/10.2307\/2275188","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}