{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T11:42:39Z","timestamp":1698061359474},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11699,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A semantics for the lambda-calculus due to Friedman is used to describe a large and natural class of categorical recursion-theoretic notions. It is shown that if <jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub> are g\u00f6del numbers for partial recursive functions in two standard <jats:italic>\u03c9<\/jats:italic>-URS's which both act like the same closed lambda-term, then there is an isomorphism of the two <jats:italic>\u03c9<\/jats:italic>-URS's which carries <jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub> to <jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub>.<\/jats:p>","DOI":"10.2307\/2273382","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:58:32Z","timestamp":1146952712000},"page":"67-83","source":"Crossref","is-referenced-by-count":3,"title":["Recursion theory and the lambda-calculus"],"prefix":"10.1017","volume":"47","author":[{"given":"Robert E.","family":"Byerly","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044716_ref006","first-page":"225","volume":"37","author":"Goodman","year":"1972","journal-title":"A simplification of combinatory logic"},{"key":"S0022481200044716_ref009","first-page":"1","article-title":"Uniformly reflexive structures: On the nature of g\u00f6delizations and relative computability","volume":"144","author":"Wagner","year":"1969","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200044716_ref007","article-title":"The independence of control structures in theoretical programming systems","author":"Riccardi","journal-title":"Journal of Computer and Systems Sciences"},{"key":"S0022481200044716_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200044716_ref004","volume-title":"The calculi of lambda conversion","author":"Church","year":"1941"},{"key":"S0022481200044716_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71229-1"},{"key":"S0022481200044716_ref008","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200044716_ref001","unstructured":"Byerly R. , Contributions to axiomatic recursion theory, Ph.D. dissertation, State University of New York at Buffalo, 1979."},{"key":"S0022481200044716_ref002","first-page":"48","volume":"47","author":"Byerly","year":"1982","journal-title":"An invariance notion in recursion theory"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044716","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:42:53Z","timestamp":1558734173000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044716\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["S0022481200044716"],"URL":"https:\/\/doi.org\/10.2307\/2273382","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,3]]}}}