{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T13:26:57Z","timestamp":1648992417388},"reference-count":1,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15807,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1970,12]]},"abstract":"<jats:p>The enumeration, given a first-order sentence <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200089386_inline01\" \/>, of all sentences deducible from <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200089386_inline02\" \/> in the first-order predicate calculus, and the enumeration, given a non-negative integer <jats:italic>n<\/jats:italic>, of the recursively enumerable set <jats:italic>W<jats:sub>n<\/jats:sub>,<\/jats:italic> are two well-known examples of effective processes. But are these processes really distinct? Indeed, might there not exist a G\u00f6del numbering of the sentences of first-order logic such that for each <jats:italic>n<\/jats:italic>, if <jats:italic>n<\/jats:italic> is the number assigned to the sentence <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200089386_inline03\" \/>, then <jats:italic>W<jats:sub>n<\/jats:sub><\/jats:italic> is the set of numbers assigned to all sentences deducible from <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200089386_inline04\" \/>? If this were the case, the first sort of enumeration would just be a particular instance of the second.<\/jats:p>","DOI":"10.2307\/2271441","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:04:20Z","timestamp":1146935060000},"page":"556-558","source":"Crossref","is-referenced-by-count":0,"title":["Recursion theory and formal deducibility"],"prefix":"10.1017","volume":"35","author":[{"given":"E. M.","family":"Kleinberg","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200089386_ref001","volume-title":"Theory of recursive functions and effective compatability","author":"Rogers","year":"1968"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200089386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T16:40:09Z","timestamp":1559320809000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200089386\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1970,12]]},"references-count":1,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1970,12]]}},"alternative-id":["S0022481200089386"],"URL":"https:\/\/doi.org\/10.2307\/2271441","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1970,12]]}}}