{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T12:08:33Z","timestamp":1765886913559},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":17358,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1966,9,2]]},"abstract":"<jats:p>The purpose of the present paper is to introduce a generalisation of the concept of productive set introduced by Post (2) and studied by Dekker (3) and others. Throughout the paper we shall use small Latin letters to denote both non-negative integers (referred to as numbers) and functions (both partial and total) from numbers to numbers. Sets of numbers will be denoted by small Greek letters and classes of such sets by capital Latin letters. <jats:italic>\u03c9<jats:sub>\u03b7<\/jats:sub><\/jats:italic> is the range of the <jats:italic>\u03b7<\/jats:italic>th partial recursive function.<\/jats:p>","DOI":"10.2307\/2270460","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:34:36Z","timestamp":1146947676000},"page":"455-459","source":"Crossref","is-referenced-by-count":2,"title":["A generalisation of productive set"],"prefix":"10.1017","volume":"31","author":[{"given":"R.","family":"Mitchell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200066846_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1944-08111-1"},{"key":"S0022481200066846_ref001","unstructured":"Mitchell R. , Some properties of non-recursive sets, Ph. D. Thesis, University of Newcastle upon Tyne, May 1962."},{"key":"S0022481200066846_ref004","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19550010205"},{"key":"S0022481200066846_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1955-0067049-X"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200066846","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T20:45:22Z","timestamp":1559508322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200066846\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1966,9,2]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1966,9,2]]}},"alternative-id":["S0022481200066846"],"URL":"https:\/\/doi.org\/10.2307\/2270460","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1966,9,2]]}}}