{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:00:15Z","timestamp":1773237615401,"version":"3.50.1"},"reference-count":24,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2012,10,9]],"date-time":"2012-10-09T00:00:00Z","timestamp":1349740800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We explain how the field of logarithmic\u2010exponential series constructed in <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#bib20\">20<\/jats:ext-link> and <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#bib21\">21<\/jats:ext-link> embeds as an exponential field in any field of exponential\u2010logarithmic series constructed in <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#bib9\">9<\/jats:ext-link>, <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#bib6\">6<\/jats:ext-link>, and <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#bib13\">13<\/jats:ext-link>. On the other hand, we explain why no field of exponential\u2010logarithmic series embeds in the field of logarithmic\u2010exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non\u2010isomorphic models of Th<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$(\\mathbb {R}_{\\mbox{an, exp}})$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\"\/><\/jats:styled-content>; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.<\/jats:p>","DOI":"10.1002\/malq.201100113","type":"journal-article","created":{"date-parts":[[2012,10,9]],"date-time":"2012-10-09T11:36:19Z","timestamp":1349782579000},"page":"434-448","source":"Crossref","is-referenced-by-count":6,"title":["Comparison of exponential\u2010logarithmic and logarithmic\u2010exponential series"],"prefix":"10.1002","volume":"58","author":[{"given":"Salma","family":"Kuhlmann","sequence":"first","affiliation":[]},{"given":"Marcus","family":"Tressl","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,9]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1962-0141661-0"},{"key":"e_1_2_13_3_1","doi-asserted-by":"crossref","first-page":"169","DOI":"10.4064\/fm-124-2-169-186","article-title":"The limit behaviour of exponential terms","volume":"124","author":"Dahn B.","year":"1984","journal-title":"Fundam. 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Papers from the special semester (RAGOS) and AMS Special Session on Real Algebraic Geometry and Ordered Algebraic Structures held at Louisiana State University, Baton Rouge, LA, January\u2013May and April 17\u201321, 1996.","author":"Kuhlmann F.\u2010V.","year":"2000"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03964-6"},{"key":"e_1_2_13_10_1","volume-title":"Ordered Exponential Fields, Fields Institute Monograph Series Vol. 12","author":"Kuhlmann S.","year":"2000"},{"key":"e_1_2_13_11_1","doi-asserted-by":"publisher","DOI":"10.2478\/s11533-010-0070-z"},{"key":"e_1_2_13_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.07.023"},{"key":"e_1_2_13_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.11.024"},{"key":"e_1_2_13_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.04.001"},{"key":"e_1_2_13_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095664"},{"key":"e_1_2_13_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90017-G"},{"key":"e_1_2_13_17_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1949-0032593-5"},{"key":"e_1_2_13_18_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1987-0869411-2"},{"key":"e_1_2_13_19_1","unstructured":"M.Schmeling Corps de Transs\u00e9ries Ph. 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