{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T07:49:00Z","timestamp":1723276140643},"reference-count":24,"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":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove quantifier elimination for the field \u211a<jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>((<jats:italic>t<\/jats:italic><jats:sup>\u211a<\/jats:sup>)) (the completion of the field of Puiseux series over \u211a<jats:sub>p<\/jats:sub>) in Macintyre's language together with symbols for functions in a class containing both <jats:italic>t<\/jats:italic>-adically and <jats:italic>p<\/jats:italic>-adically overconvergent functions. We also show that the theory of \u211a<jats:italic>p<\/jats:italic>((<jats:italic>t<\/jats:italic><jats:sup>\u211a<\/jats:sup>)) is <jats:italic>b<\/jats:italic>-minimal in this language.<\/jats:p>","DOI":"10.2178\/jsl\/1278682201","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T09:30:45Z","timestamp":1278667845000},"page":"802-816","source":"Crossref","is-referenced-by-count":1,"title":["<i>p<\/i>-adically closed fields with nonstandard analytic structure"],"prefix":"10.1017","volume":"75","author":[{"given":"Ali","family":"Bleybel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002395_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0071461"},{"key":"S0022481200002395_ref003","unstructured":"Cluckers R. and Lipshitz L. , Fields with analytic structure, preprint, 2007."},{"key":"S0022481200002395_ref023","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/131.3\/1175894"},{"key":"S0022481200002395_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1971463"},{"key":"S0022481200002395_ref010","volume-title":"G\u00e9om\u00e9trie analytique rigide et applications","author":"Fresnel","year":"1981"},{"key":"S0022481200002395_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389133"},{"key":"S0022481200002395_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdn024"},{"key":"S0022481200002395_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/1971135"},{"key":"S0022481200002395_ref004","first-page":"535","volume":"39","author":"Cluckers","year":"2006","journal-title":"Analytic cell decomposition and analytic motivic integration, Annales Scientifiques de l'\u00c9cole Normale Sup\u00e9rieure"},{"key":"S0022481200002395_ref014","first-page":"605","volume":"41","author":"Macintyre","year":"1976","journal-title":"On definable subsets of p-adic fields"},{"key":"S0022481200002395_ref002","first-page":"262","article-title":"A note on the p-adic convergence of solutions of linear differential equations","volume":"17","author":"Clark","year":"1966","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200002395_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-52229-1"},{"key":"S0022481200002395_ref013","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609306018832"},{"key":"S0022481200002395_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65505-0"},{"key":"S0022481200002395_ref015","first-page":"137","article-title":"Uniform p-adic cell decomposition and local zeta functions","volume":"399","author":"Pas","year":"1989","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"S0022481200002395_ref016","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-60.1.37"},{"key":"S0022481200002395_ref019","unstructured":"Schoutens H. , Approximation and subanalytic sets over a complete valuation ring, Ph.D. thesis, Catholic University of Leuven, 1991."},{"key":"S0022481200002395_ref006","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061307000664"},{"key":"S0022481200002395_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799007358"},{"key":"S0022481200002395_ref018","volume-title":"Ultrametric calculus. 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