{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:00:29Z","timestamp":1773237629735,"version":"3.50.1"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6310,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the model theory of fields <jats:italic>k<\/jats:italic> carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove that the definable real valuation rings of <jats:italic>k<\/jats:italic> are in correspondence with the definable convex subgroups of the value group of a certain real valuation of <jats:italic>k<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2275808","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:54Z","timestamp":1146956394000},"page":"1121-1152","source":"Crossref","is-referenced-by-count":12,"title":["Some model theory for almost real closed fields"],"prefix":"10.1017","volume":"61","author":[{"given":"Fran\u00e7oise","family":"Delon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafel","family":"Farr\u00e9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200016819_ref029","first-page":"269","article-title":"Einige unentscheidbare K\u00f6rpertheorien","volume":"XXVIII","author":"Ziegler","year":"1982","journal-title":"L'enseignement math\u00e9matique"},{"key":"S0022481200016819_ref027","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099397"},{"key":"S0022481200016819_ref025","doi-asserted-by":"publisher","DOI":"10.4064\/fm-41-2-203-271"},{"key":"S0022481200016819_ref024","first-page":"1","article-title":"Chain signatures and real closures","volume":"347","author":"Schwartz","year":"1984","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200016819_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0101548"},{"key":"S0022481200016819_ref017","first-page":"181","article-title":"On places of algebraic function fields","volume":"353","author":"Kuhlmann","year":"1984","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200016819_ref016","first-page":"314","article-title":"Bewertungen mit reeller Henselisierung","volume":"286","author":"Knebusch","year":"1976","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200016819_ref019","volume-title":"Th\u00e9orie des Valuations","author":"Ribenboim","year":"1964"},{"key":"S0022481200016819_ref014","unstructured":"Jacob B. , The model theory of Pythagorean fields, Ph.D. thesis , Princeton, 1979."},{"key":"S0022481200016819_ref012","first-page":"165","article-title":"Elementary properties of ordered Abelian groups","volume":"46","author":"Gurevich","year":"1965","journal-title":"Translations of the American Mathematical Society"},{"key":"S0022481200016819_ref011","doi-asserted-by":"publisher","DOI":"10.4064\/fm-47-1-57-103"},{"key":"S0022481200016819_ref010","first-page":"915","volume":"58","author":"Farr\u00e9","year":"1993","journal-title":"A transfer theorem for henselian valued and ordered fields"},{"key":"S0022481200016819_ref007","first-page":"315","volume-title":"Proceedings of the American Mathematical Society","author":"Delon","year":"1986"},{"key":"S0022481200016819_ref008","first-page":"499","volume":"54","author":"Delon","year":"1989","journal-title":"Inclusions et produits de groupes ab\u00e9liens ordonn\u00e9s \u00e9tudi\u00e9s au premier ordre"},{"key":"S0022481200016819_ref005","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200016819_ref003","unstructured":"Becker E. , Berr R. , and Gondard D. , Henselian fields with real-closed residue field, preprint."},{"key":"S0022481200016819_ref001","volume-title":"Hereditarily-Pythagorean fields and orderings of higher level","author":"Becker","year":"1978"},{"key":"S0022481200016819_ref004","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1215\/ijm\/1256044752","article-title":"Ordered fields satisfying Rolle's theorem","author":"Brown","year":"1986","journal-title":"Illinois Journal of Mathematics"},{"key":"S0022481200016819_ref026","unstructured":"van den Dries L. , Model theory of fields, Ph.D. thesis , Utrecht, 1978."},{"key":"S0022481200016819_ref028","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1961-0120294-X"},{"key":"S0022481200016819_ref020","unstructured":"Schmitt P. H. , Elementary properties of ordered abelian groups, preprint."},{"key":"S0022481200016819_ref023","first-page":"65","volume-title":"Signatures and real closures of a field","volume":"1","author":"Schwartz"},{"key":"S0022481200016819_ref006","volume-title":"Th\u00e8se d'\u00e9tat","author":"Delon","year":"1982"},{"key":"S0022481200016819_ref009","doi-asserted-by":"crossref","unstructured":"Farr\u00e9 R. , Some model theory for valued and ordered fields, and applications, 1993.","DOI":"10.2307\/2275104"},{"key":"S0022481200016819_ref013","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/008\/653181"},{"key":"S0022481200016819_ref015","first-page":"213","article-title":"The model theory of generalized real-closed fields","volume":"323","author":"Jacob","year":"1981","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200016819_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099396"},{"key":"S0022481200016819_ref022","volume-title":"Habilitationsschrift","author":"Schmitt","year":"1982"},{"key":"S0022481200016819_ref002","first-page":"8","article-title":"Summen n-ter Potenzen in K\u00f6rpern","volume":"307","author":"Becker","year":"1979","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016819","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:59:49Z","timestamp":1557691189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016819\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0022481200016819"],"URL":"https:\/\/doi.org\/10.2307\/2275808","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}