{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T11:33:06Z","timestamp":1753356786532},"reference-count":4,"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":9781,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1987,6]]},"abstract":"<jats:p>Dans Poizat [1981], le second auteur a montr\u00e9 qu'un sous-groupe infiniment d\u00e9finissable d'un groupe stable \u00e9tait intersection de sous-groupes d\u00e9finissables; il a pos\u00e9 la question de savoir si une relation d'\u00e9quivalence <jats:italic>E<\/jats:italic>, infiniment d\u00e9finissable dans un mod\u00e8le <jats:italic>M<\/jats:italic> d'une th\u00e9orie stable <jats:italic>T<\/jats:italic>, \u00e9tait conjonction de relations d'\u00e9quivalence d\u00e9finissables. Nous allons voir ici que c'est presque exact: c'est vrai si <jats:italic>T<\/jats:italic> est totalement transcendante, et, dans le cas g\u00e9n\u00e9ral de stabilit\u00e9 <jats:italic>E<\/jats:italic> a toujours un raffinement <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub> (plus pr\u00e9cis\u00e9ment, <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub> est la conjonction de <jats:italic>E<\/jats:italic> et de la relation \u201c<jats:italic>x<\/jats:italic> et <jats:italic>y<\/jats:italic> ont m\u00eame type\u201d) qui a cette propri\u00e9t\u00e9; cela montre que cette relation <jats:italic>E<\/jats:italic> n'introduit pas d'imaginaires d'une nature vraiment diff\u00e9rente de celle des imaginaires de Shelah: dans une th\u00e9orie stable, un imaginaire infinitaire n'est rien d'autre qu'un ensemble d'imaginaires finis.<\/jats:p><jats:p>La d\u00e9monstration du th\u00e9or\u00e8me principal de cette note s'appuie lourdement sur la construction <jats:italic>M<\/jats:italic><jats:sup>eq<\/jats:sup> de Shelah, la machinerie de la d\u00e9viation, les param\u00e8tres imaginaires canoniques pour la d\u00e9finition d'un type stable, etc\u2026. Pour tout cela, les r\u00e9f\u00e9rences ad\u00e9quates sont Shelah [1978], Pillay [1983], et Poizat [1985, Chapitre 16].<\/jats:p><jats:p>Nouscommen\u00e7ons par pr\u00e9ciser ce que nous entendons par \u201crelation d'\u00e9quivalence infiniment d\u00e9finissable\u201d: une collection de formules <jats:italic>e(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200034368_inline1\" \/><\/jats:italic>, <jats:italic>\u0233<\/jats:italic>), <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200034368_inline1\" \/> et <jats:italic>\u0233<\/jats:italic> \u00e9tant de longueur <jats:italic>n<\/jats:italic>, telle que, pour tout mod\u00e8le <jats:italic>M<\/jats:italic> de <jats:italic>T<\/jats:italic>, les couples (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200034368_inline1\" \/>, <jats:italic>\u0233<\/jats:italic>) qui les satisfont toutes forment une r\u00e9lation d'\u00e9quivalence <jats:italic>E<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2274390","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:21:40Z","timestamp":1146954100000},"page":"400-403","source":"Crossref","is-referenced-by-count":9,"title":["Pas d'imaginaires dans l'infini!"],"prefix":"10.1017","volume":"52","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]},{"given":"Bruno","family":"Poizat","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200034368_ref002","first-page":"137","volume":"46","author":"Poizat","year":"1981","journal-title":"Sous-groupes definissables d'un groupe stable"},{"key":"S0022481200034368_ref001","volume-title":"An introduction to stability theory","author":"Pillay","year":"1983"},{"key":"S0022481200034368_ref003","volume-title":"Cours de th\u00e9orie des mod\u00e8les","author":"Poizat","year":"1985"},{"key":"S0022481200034368_ref004","volume-title":"Classification theory and the number of nonisomorphic models","author":"Shelah","year":"1978"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200034368","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T19:47:54Z","timestamp":1558468074000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200034368\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,6]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1987,6]]}},"alternative-id":["S0022481200034368"],"URL":"https:\/\/doi.org\/10.2307\/2274390","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,6]]}}}