{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T07:52:09Z","timestamp":1648540329508},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":649,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In 1984, Henson and Rubel [2] proved the following theorem: If <jats:italic>p(x<jats:sub>1<\/jats:sub>,\u2026, x<jats:sub>n<\/jats:sub>)<\/jats:italic> is an exponential polynomial with coefficients in \u2102 with no zeroes in \u2102, then <jats:italic>p(x<jats:sub>1<\/jats:sub>,\u2026, x<jats:sub>n<\/jats:sub>)<\/jats:italic> = <jats:italic>e<jats:sup>g(x<jats:sub>1<\/jats:sub>,\u2026, x<jats:sub>n<\/jats:sub>)<\/jats:sup><\/jats:italic> where <jats:italic>g(x<jats:sub>1<\/jats:sub>,\u2026, x<jats:sub>n<\/jats:sub>)<\/jats:italic> is some exponential polynomial over C. In this paper, I will prove the analog of this theorem for Zilber's Pseudoexponential fields directly from the axioms. Furthermore, this proof relies only on the existential closedness axiom without any reference to Schanuel's conjecture.<\/jats:p>","DOI":"10.2178\/jsl\/1333566630","type":"journal-article","created":{"date-parts":[[2012,4,4]],"date-time":"2012-04-04T15:26:53Z","timestamp":1333553213000},"page":"423-432","source":"Crossref","is-referenced-by-count":1,"title":["Henson and Rubel's theorem for Zilber's pseudoexponentiation"],"prefix":"10.1017","volume":"77","author":[{"family":"Ahuva C. Shkop","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000669_ref002","first-page":"1","article-title":"Some applications of Nevanlinna theory to mathematical logic: identities of exponential functions","volume":"282","author":"Henson","year":"1984","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200000669_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.07.001"},{"key":"S0022481200000669_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm207-2-2"},{"key":"S0022481200000669_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90017-G"},{"key":"S0022481200000669_ref004","first-page":"791","volume":"71","author":"Marker","year":"2006","journal-title":"Remarks on Zilber's pseudoexponentiation"},{"key":"S0022481200000669_ref005","volume-title":"Basic algebraic geometry","author":"Shafarevich","year":"1995"},{"key":"S0022481200000669_ref006","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1984.113.51"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000669","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T16:46:58Z","timestamp":1556210818000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000669\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["S0022481200000669"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1333566630","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}