{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:35:25Z","timestamp":1773149725910,"version":"3.50.1"},"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":17268,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1966,12]]},"abstract":"<jats:p>In this note is proved the following:<\/jats:p><jats:p>Theorem.<jats:italic>I\u0192 A \u00d7 B is universal and one o\u0192 A, B is r.e. then one of A, B is universal<\/jats:italic>.<\/jats:p><jats:p>Let<jats:italic>\u03b1, \u03c4<\/jats:italic>be 1-argument recursive functions such that<jats:italic>x<\/jats:italic>goes to (<jats:italic>\u03c3(\u03c7), \u03c4(\u03c7)<\/jats:italic>) is a (1\u20131) map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is called<jats:italic>universal<\/jats:italic>if every r.e. set is (many-one) reducible to A; A \u00d7 B is called<jats:italic>universal<\/jats:italic>if the set<\/jats:p>","DOI":"10.2307\/2269692","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:36:19Z","timestamp":1146947779000},"page":"573-574","source":"Crossref","is-referenced-by-count":26,"title":["A note on universal sets"],"prefix":"10.1017","volume":"31","author":[{"given":"A. H.","family":"Lachlan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200066019_ref001","doi-asserted-by":"crossref","DOI":"10.1515\/9781400882007","volume-title":"Theory of Formal Systems","author":"Smullyan","year":"1961"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200066019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T14:15:15Z","timestamp":1586873715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200066019\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1966,12]]},"references-count":1,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1966,12]]}},"alternative-id":["S0022481200066019"],"URL":"https:\/\/doi.org\/10.2307\/2269692","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1966,12]]}}}