{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:24:44Z","timestamp":1775643884622,"version":"3.50.1"},"reference-count":7,"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":10876,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,6]]},"abstract":"<jats:p>Un espace ultram\u00e9trique est un ensemble muni d'une distance \u00e0 valeurs dans un ordre total avec premier \u00e9l\u00e9ment et pour laquelle tout triangle est isoc\u00e8le avex deux grands c\u00f4t\u00e9s \u00e9gaux. Les deux cas importants d'espaces ultram\u00e9triques sont:<\/jats:p><jats:p>(1) les corps valu\u00e9s lorsqu'on ne consid\u00e8re que leur structure m\u00e9trique, et<\/jats:p><jats:p>(2) les ensembles <jats:italic>A<jats:sup>\u03bb<\/jats:sup><\/jats:italic>, o\u00f9 <jats:italic>\u03bb<\/jats:italic> est un ensemble bien ordonn\u00e9, munis de la distance <jats:italic>d<\/jats:italic>(<jats:italic>\u03b1, \u03b2<\/jats:italic>) = inf {<jats:italic>\u03b3<\/jats:italic> \u2208 <jats:italic>\u03bb; \u03b1<\/jats:italic>(<jats:italic>\u03b3<\/jats:italic>) \u2260 <jats:italic>\u03b2<\/jats:italic>(<jats:italic>\u03b3<\/jats:italic>)} si <jats:italic>\u03b1<\/jats:italic> \u2260 <jats:italic>\u03b2<\/jats:italic> et <jats:italic>d<\/jats:italic>(<jats:italic>\u03b1, \u03b2<\/jats:italic>) = 0 sinon; distance \u00e0 valeurs dans l'ordre inverse de <jats:italic>\u03bb<\/jats:italic> enrichi d'un premier \u00e9l\u00e9ment 0.<\/jats:p><jats:p>Nous \u00e9tudions ces structures dans un langage comportant un seul type de variables, les points de l'espace, et un pr\u00e9dicat \u00e0 quatre places traduisant l'ordre sur les distances<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200033466_eqnU1\"\/><\/jats:disp-formula><\/jats:p><jats:p>Nous d\u00e9finissons la notion d'espace riche, qui est la mod\u00e8le-compl\u00e9tion relative \u00e0 un ensemble des distances fix\u00e9: un espace est riche si et seulement s'il est existentiellement clos dans toute extension qui n'ajoute pas de nouvelle distance. Les deux exemples pr\u00e9c\u00e9demment donn\u00e9s, espaces <jats:italic>A<\/jats:italic><jats:sup>\u03bb<\/jats:sup> et corps valu\u00e9s, fournissent des espaces riches. La suite de l'article s'attache \u00e0 la description des espaces riches.<\/jats:p>","DOI":"10.2307\/2274173","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:08:28Z","timestamp":1146953308000},"page":"405-424","source":"Crossref","is-referenced-by-count":11,"title":["Espaces ultram\u00e9triques"],"prefix":"10.1017","volume":"49","author":[{"given":"Fran\u00e7oise","family":"Delon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200033466_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(80)90009-1"},{"key":"S0022481200033466_ref002","first-page":"481","volume":"43","author":"Keisler","year":"1978","journal-title":"The stability function of a theory"},{"key":"S0022481200033466_ref006","first-page":"215","volume":"44","author":"Shelah","year":"1979","journal-title":"On uniqueness of prime models"},{"key":"S0022481200033466_ref005","first-page":"513","volume":"46","author":"Poizat","year":"1981","journal-title":"Th\u00e9ories instables"},{"key":"S0022481200033466_ref004","first-page":"1981","volume-title":"Groupe d'\u00e9tude de th\u00e9ories stables. Ire ann\u00e9e: 1977\/78; 2e ann\u00e9e: 1978\/79","author":"Poizat","year":"1978"},{"key":"S0022481200033466_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079095"},{"key":"S0022481200033466_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018541"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200033466","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T20:48:36Z","timestamp":1558644516000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200033466\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1984,6]]}},"alternative-id":["S0022481200033466"],"URL":"https:\/\/doi.org\/10.2307\/2274173","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,6]]}}}