{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T08:48:10Z","timestamp":1773218890844,"version":"3.50.1"},"reference-count":12,"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":3388,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if <jats:italic>F<\/jats:italic> is a countable, recursive and perfect field of positive characteristic <jats:italic>p<\/jats:italic>, with decidable theory, then the structure of addition, the Frobenius map <jats:italic>x<\/jats:italic> \u2192 <jats:italic>x<\/jats:italic><jats:italic><jats:sup>p<\/jats:sup><\/jats:italic> and the property <jats:italic>\u2018x<\/jats:italic> \u2208 <jats:italic>F<jats:sup>1<\/jats:sup><\/jats:italic>, over the ring of polynomials <jats:italic>F[T]<\/jats:italic>, has a decidable theory.<\/jats:p>","DOI":"10.2178\/jsl\/1102022210","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:48:22Z","timestamp":1109800102000},"page":"1006-1026","source":"Crossref","is-referenced-by-count":5,"title":["Elimination theory for addition and the frobenius map in polynomial rings"],"prefix":"10.1017","volume":"69","author":[{"given":"Thanases","family":"Pheidas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karim","family":"Zahidi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007386_ref007","unstructured":"Pheidas T. , The diophantine problem for addition and divisibility in polynomial rings, Ph.D. thesis , Purdue University, 1985."},{"key":"S0022481200007386_ref001","first-page":"1\u20139","volume-title":"Model theory of algebra and arithmetic (Proceedings of conference, Karpacz, 1979)","volume":"834","author":"Becker","year":"1980"},{"key":"S0022481200007386_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(84)90014-9"},{"key":"S0022481200007386_ref002","first-page":"102\u2013112","volume-title":"Models and sets","volume":"1103","author":"Cherlin","year":"1984"},{"key":"S0022481200007386_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600562"},{"key":"S0022481200007386_ref008","first-page":"49\u2013105","article-title":"Undecidability of existential theories of rings and fields: a survey","volume":"270","author":"Pheidas","year":"1999","journal-title":"Contemporary Mathematics"},{"key":"S0022481200007386_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1978-0491583-7"},{"key":"S0022481200007386_ref011","first-page":"71\u201379","article-title":"Images of additive polynomials in F((t)) have the optimal approximation property","volume":"45","author":"van den Dries","year":"2002","journal-title":"Canadian Mathematical Bulletin, Bulletin Canadien de Mathematiques"},{"key":"S0022481200007386_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1951-0041081-0"},{"key":"S0022481200007386_ref006","volume-title":"A shorter model theory","author":"Hodges","year":"1997"},{"key":"S0022481200007386_ref003","first-page":"997\u20131015","volume":"67","author":"Dellunde","year":"2002","journal-title":"The theory of modules of separably closed fields, I"},{"key":"S0022481200007386_ref005","first-page":"131\u2013145","volume-title":"Logic colloquium \u201978 (Mons, 1978)","volume":"97","author":"Denef","year":"1979"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T19:38:37Z","timestamp":1557171517000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007386\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,12]]}},"alternative-id":["S0022481200007386"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1102022210","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}