{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T22:37:00Z","timestamp":1773268620032,"version":"3.50.1"},"reference-count":10,"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":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:p>In [10] we introduced a new first order language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> for valued fields. This language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> has three sorts of variables, namely variables for elements of the valued field, variables for elements of the residue field and variables for elements of the value group. <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> contains symbols for the standard field, residue field, and value group operations and a function symbol for the valuation. Essential in our language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> is a function symbol for an angular component map modulo <jats:italic>P<\/jats:italic>, which is a map from the field to the residue field (see Definition 1.2).<\/jats:p><jats:p>For this language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> we proved a quantifier elimination theorem for Henselian valued fields of equicharacteristic zero which possess such an angular component map modulo <jats:italic>P<\/jats:italic> [10, Theorem 4.1]. In the first section of this paper we give some partial results on the existence of an angular component map modulo <jats:italic>P<\/jats:italic> on an arbitrary valued field.<\/jats:p><jats:p>By applying the above quantifier elimination theorem to ultraproducts <jats:bold>\u03a0Q<\/jats:bold><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>\/<jats:italic>D<\/jats:italic>, we obtained a quantifier elimination, in the language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/>, for the <jats:italic>p<\/jats:italic>-adic field <jats:bold>Q<\/jats:bold><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>; and this elimination is uniform for almost all primes <jats:italic>p<\/jats:italic> [10, Corollary 4.3]. In \u00a72 we prove that our language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025597_inline1\"\/> is essentially stronger than the natural language for <jats:italic>p<\/jats:italic>-adic fields in the sense that the angular component map modulo <jats:italic>P<\/jats:italic> cannot be defined, uniformly for almost all <jats:italic>p<\/jats:italic>, in terms of the natural language for <jats:italic>p<\/jats:italic>-adic fields.<\/jats:p>","DOI":"10.2307\/2274477","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:36:50Z","timestamp":1146940610000},"page":"1125-1129","source":"Crossref","is-referenced-by-count":16,"title":["On the angular component map modulo <i>P<\/i>"],"prefix":"10.1017","volume":"55","author":[{"given":"Johan","family":"Pas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025597_ref010","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":"S0022481200025597_ref009","volume-title":"Model theory audits applications","author":"Kopperman","year":"1972"},{"key":"S0022481200025597_ref008","first-page":"384","volume-title":"Logic conference, Kiel 1974","volume":"499","author":"Kochen","year":"1975"},{"key":"S0022481200025597_ref007","volume-title":"Infinite abelian groups","author":"Fuchs","year":"1970"},{"key":"S0022481200025597_ref006","volume-title":"A mathematical introduction to logic","author":"Enderton","year":"1972"},{"key":"S0022481200025597_ref005","first-page":"154","article-title":"p-adic semi-algebraic sets and cell decomposition","volume":"369","author":"Denef","year":"1986","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"S0022481200025597_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079565"},{"key":"S0022481200025597_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200025597_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2373066"},{"key":"S0022481200025597_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/020\/0316419"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025597","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:25:36Z","timestamp":1558196736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025597\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0022481200025597"],"URL":"https:\/\/doi.org\/10.2307\/2274477","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}