{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T08:57:59Z","timestamp":1760345879462},"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":8777,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,3]]},"abstract":"Un prolongement de l'\u00e9tude d'une th\u00e9orie T<\/jats:italic>, dans le langage , consiste \u00e0 s'int\u00e9resser \u00e0 la th\u00e9orie T<\/jats:italic>* des paires de mod\u00e8les de T<\/jats:italic>, c'est-\u00e0-dire les structures de la forme (K<\/jats:italic> \u228a L<\/jats:italic>) o\u00f9 K<\/jats:italic> \u22a8 T<\/jats:italic>, L<\/jats:italic> \u22a8 T, K<\/jats:italic> \u227a L<\/jats:italic>, dans le langage o\u00f9 E<\/jats:italic> est un pr\u00e9dicat pour la sous-structure. Les propri\u00e9t\u00e9s de la th\u00e9orie T ne se transmettent pas toujours \u00e0 T<\/jats:italic>*, particuli\u00e8rement en ce qui concerne la compl\u00e9tude et la d\u00e9cidabilit\u00e9. On trouve des illustrations de cas oppos\u00e9s dans les th\u00e9ories de corps:<\/jats:p>\u2014si T<\/jats:italic> est la th\u00e9orie des corps alg\u00e9briquement clos de caract\u00e9ristique fix\u00e9e, T<\/jats:italic>* est compl\u00e8te et d\u00e9cidable;<\/jats:p>\u2014si T<\/jats:italic> est la th\u00e9orie des corps r\u00e9els clos, T<\/jats:italic> est compl\u00e8te et d\u00e9cidable, mais T<\/jats:italic>* est ind\u00e9cidable, et admet compl\u00e9tions diff\u00e9rentes.<\/jats:p>Nous allons nous int\u00e9resser ici aux paires de corps valu\u00e9s henseliens, et plus particuli\u00e8rement au cas de caract\u00e9ristique r\u00e9siduelle nulle, de la forme (K \u228a L<\/jats:italic>, \u03c5) o\u00f9 (K<\/jats:italic>, \u03c5) n'est pas n\u00e9cessairement une sous-structure \u00e9l\u00e9mentaire de (L<\/jats:italic>, \u03c5). Ax, Kochen et Ershov ont montr\u00e9 que la th\u00e9orie d'un corps valu\u00e9 henselien de caract\u00e9ristique r\u00e9siduelle nulle est enti\u00e8rement d\u00e9termin\u00e9e par la th\u00e9orie de son corps de restes et par la th\u00e9orie de son groupe de valuation; par ailleurs, de r\u00e9sultats analogues existent pour certains corps de caract\u00e9ristique r\u00e9siduelle non nulle.<\/jats:p>","DOI":"10.2307\/2274971","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:33:48Z","timestamp":1146940428000},"page":"323-339","source":"Crossref","is-referenced-by-count":2,"title":["Th\u00e9ories compl\u00e8tes de paires de corps valu\u00e9s henseliens"],"prefix":"10.1017","volume":"55","author":[{"given":"G\u00e9rard","family":"Leloup","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026608_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200026608_ref008","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1307\/mmj\/1028999037","article-title":"Complete theories of algebraically closed fields with distinguished subfields","volume":"11","author":"Keisler","year":"1964","journal-title":"Michigan Mathematical Journal"},{"key":"S0022481200026608_ref002","first-page":"669","volume":"47","author":"Baur","year":"1982","journal-title":"On the theory of pairs of real closed fields. II"},{"key":"S0022481200026608_ref001","first-page":"25","volume-title":"Logic and algorithmic (in honour of E. Specker)","volume":"30","author":"Baur","year":"1982"},{"key":"S0022481200026608_ref004","first-page":"421","volume":"53","author":"Delon","year":"1988","journal-title":"Extensions separ\u00e9es et imm\u00e9diates de corps valu\u00e9s"},{"key":"S0022481200026608_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079426"},{"key":"S0022481200026608_ref005","unstructured":"Delon F. , Ind\u00e9cidabilit\u00e9 de la th\u00e9orie des paires imm\u00e9diates de corps valu\u00e9s henseliens, manuscrit."},{"key":"S0022481200026608_ref006","volume-title":"Groupe d'\u00c9tude de Th\u00e9ories Stables","author":"Delon","year":"1981"},{"key":"S0022481200026608_ref007","volume-title":"Cours manuscrit sur la th\u00e9orie des mod\u00e8les","author":"Delon","year":"1983"},{"key":"S0022481200026608_ref010","unstructured":"Macintyre A. J. , Classifying pairs of real closed fields, Ph.D. thesis, Stanford University, Stanford, California, 1968."},{"key":"S0022481200026608_ref011","first-page":"358","volume":"34","author":"Macintyre","year":"1969","journal-title":"Complete theories of topological fields with distinguished dense proper subfields"},{"key":"S0022481200026608_ref012","volume-title":"Th\u00e9orie des valuations","author":"Ribenboim","year":"1964"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026608","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T17:52:26Z","timestamp":1558201946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026608\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["S0022481200026608"],"URL":"https:\/\/doi.org\/10.2307\/2274971","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}