{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T01:46:01Z","timestamp":1648691161082},"reference-count":0,"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":18639,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1963,3]]},"abstract":"<jats:p>This note will characterize those partial functions which are partial recursive under an arbitrary \u201crenaming\u201d of the integers.<\/jats:p><jats:p>The formal result. Let <jats:italic>I<\/jats:italic> be the non-negative integers. For any partial function <jats:italic>f<\/jats:italic> on <jats:italic>I<\/jats:italic> into <jats:italic>I<\/jats:italic>, and for any permutation <jats:italic>\u03c3<\/jats:italic> of <jats:italic>I<\/jats:italic>, let <jats:italic>f<jats:sub>\u03c3<\/jats:sub><\/jats:italic> be the partial function which <jats:italic>f<\/jats:italic> becomes when the integers are renamed according to <jats:italic>\u03c3<\/jats:italic>. That is, let <jats:italic>f<jats:sub>\u03c3<\/jats:sub><\/jats:italic> = <jats:italic>\u03c3f\u03c3<\/jats:italic><jats:sup>\u22121<\/jats:sup> in the sense that <jats:italic>f<jats:sub>\u03c3<\/jats:sub><\/jats:italic>(<jats:italic>x<\/jats:italic>) is defined whenever <jats:italic>\u03c3<\/jats:italic><jats:sup>\u22121<\/jats:sup>(<jats:italic>\u0445<\/jats:italic>) \u220a Dom <jats:italic>f<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2271332","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:20:24Z","timestamp":1146932424000},"page":"17-19","source":"Crossref","is-referenced-by-count":0,"title":["Functions which remain partial recursive under all similarity transformations"],"prefix":"10.1017","volume":"28","author":[{"given":"Norman","family":"Shapiro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200115506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T15:31:44Z","timestamp":1559662304000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200115506\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1963,3]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1963,3]]}},"alternative-id":["S0022481200115506"],"URL":"https:\/\/doi.org\/10.2307\/2271332","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1963,3]]}}}