{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T04:32:16Z","timestamp":1649133136064},"reference-count":20,"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":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>K<\/jats:italic> be a computable field. Let <jats:italic>\u2131<\/jats:italic> be a collection of recursive functions over <jats:italic>K<\/jats:italic>, possibly including field operations. We investigate the following question. Given an r.e. degree <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009749_inline1\" \/>. is there an injective map <jats:italic>j<\/jats:italic> : <jats:italic>K<\/jats:italic> \u2192 \u2115 such that <jats:italic>j<\/jats:italic>(<jats:italic>K<\/jats:italic>) is of degree a and all the functions in <jats:italic>\u2131<\/jats:italic> are translated by restrictions of total recursive functions.<\/jats:p>","DOI":"10.2178\/jsl\/1190150110","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:13:31Z","timestamp":1197573211000},"page":"787-819","source":"Crossref","is-referenced-by-count":0,"title":["Generalised weak presentations"],"prefix":"10.1017","volume":"67","author":[{"given":"Alexandra","family":"Shlapentokh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009749_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00074-2"},{"key":"S0022481200009749_ref019","first-page":"131","volume-title":"Recursion Theory and Complexity","author":"Shlapentokh","year":"1997"},{"key":"S0022481200009749_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760931"},{"key":"S0022481200009749_ref016","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0323"},{"key":"S0022481200009749_ref014","first-page":"1068","volume":"59","author":"Shlapentokh","year":"1994","journal-title":"Diophantine equivalence and countable rings"},{"key":"S0022481200009749_ref013","first-page":"341","article-title":"Computable algebra","volume":"95","author":"Rabin","year":"1960","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200009749_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90049-R"},{"key":"S0022481200009749_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07216-5"},{"key":"S0022481200009749_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/006"},{"key":"S0022481200009749_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00010-9"},{"key":"S0022481200009749_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00043-3"},{"key":"S0022481200009749_ref001","volume-title":"Algebraic Numbers and Algebraic Functions","author":"Artin","year":"1986"},{"key":"S0022481200009749_ref005","volume-title":"Transcendental Number Theory","author":"Baker","year":"1990"},{"key":"S0022481200009749_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90097-6"},{"key":"S0022481200009749_ref011","volume-title":"Algebraic Number Fields","author":"Januz","year":"1973"},{"key":"S0022481200009749_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00023-2"},{"key":"S0022481200009749_ref015","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1269"},{"key":"S0022481200009749_ref012","first-page":"199","volume":"60","author":"Jockusch","year":"1995","journal-title":"Weak presentations of computable fields"},{"key":"S0022481200009749_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90190-O"},{"key":"S0022481200009749_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(96)00026-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009749","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:06:27Z","timestamp":1557191187000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009749\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009749"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150110","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}