{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T00:06:31Z","timestamp":1693353991197},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7497,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In well-known papers ([A-K1], [A-K2], and [E]) J. Ax, S. Kochen, and J. Ershov prove a transfer theorem for henselian valued fields. Here we prove an analogue for henselian valued and ordered fields. The orders for which this result apply are the usual orders and also the higher level orders introduced by E. Becker in [Bl] and [B2]. With certain restrictions, two henselian valued and ordered fields are elementarily equivalent if and only if their value groups (with a little bit more structure) and their residually ordered residue fields (a henselian valued and ordered field induces in a natural way an order in its residue field) are elementarily equivalent. Similar results are proved for elementary embeddings and \u2200-extensions (extensions where the structure is existentially closed).<\/jats:p>","DOI":"10.2307\/2275104","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:49:16Z","timestamp":1146955756000},"page":"915-930","source":"Crossref","is-referenced-by-count":5,"title":["A transfer theorem for Henselian valued and ordered fields"],"prefix":"10.1017","volume":"58","author":[{"given":"Rafel","family":"Farr\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120002096X_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2373065"},{"key":"S002248120002096X_ref009","volume-title":"Model theory","volume":"73","author":"Chang","year":"1973"},{"key":"S002248120002096X_ref005","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"},{"key":"S002248120002096X_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02952512"},{"key":"S002248120002096X_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2373066"},{"key":"S002248120002096X_ref011","unstructured":"Jacob B. , The model theory of Pythagorean fields, Ph.D. Thesis, Princeton University, Princeton, 1979."},{"key":"S002248120002096X_ref004","volume-title":"Hereditarily pythagorean fields and orderings of higher level","volume":"29","author":"Becker","year":"1978"},{"key":"S002248120002096X_ref006","first-page":"53","article-title":"Signatures of fields and extension theory","volume":"330","author":"Becker","year":"1982","journal-title":"Journal f\u00fcr die reine and angewandte Mathematik"},{"key":"S002248120002096X_ref007","unstructured":"Delon F. and Farr\u00e9 R. . Some model theory for almost real closed fields, preprint, 1992."},{"key":"S002248120002096X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65505-0"},{"key":"S002248120002096X_ref010","first-page":"1390","article-title":"On the elementary theory of maximal normed fields","volume":"6","author":"Ershov","year":"1965","journal-title":"Soviet Mathematics Doklady"},{"key":"S002248120002096X_ref014","volume-title":"Th\u00e9orie des Valuations","volume":"9","author":"Ribenboim","year":"1965"},{"key":"S002248120002096X_ref012","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":"S002248120002096X_ref013","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1987.128.333"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120002096X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T22:03:38Z","timestamp":1557957818000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120002096X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["S002248120002096X"],"URL":"https:\/\/doi.org\/10.2307\/2275104","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}