{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:07:42Z","timestamp":1775642862201,"version":"3.50.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":17451,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1966,6]]},"abstract":"<jats:p>Our principal result is that there exist two incomparable recursively enumerable degrees whose greatest lower bound in the upper semilattice of degrees is <jats:bold>0<\/jats:bold>. This was conjectured by Sacks [5]. As a secondary result, we prove that on the other hand there exists a recursively enumerable degree <jats:bold>a &lt; 0<jats:sup>(1)<\/jats:sup><\/jats:bold> such that for no non-zero recursively enumerable degree <jats:bold>b<\/jats:bold> is <jats:bold>0<\/jats:bold> the greatest lower bound of <jats:bold>a<\/jats:bold> and <jats:bold>b<\/jats:bold>.<\/jats:p><jats:p>The proof of the main theorem involves a method that we have developed elsewhere [8] to deal with situations in which a partial recursive functional may interfere infinitely often with an opposed requirement of lower priority.<\/jats:p>","DOI":"10.2307\/2269807","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:33:08Z","timestamp":1146947588000},"page":"159-168","source":"Crossref","is-referenced-by-count":84,"title":["A minimal pair of recursively enumerable degrees"],"prefix":"10.1017","volume":"31","author":[{"given":"C. E. M.","family":"Yates","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200067359_ref008","unstructured":"Yates C. E. M. , On the degree of index sets, to appear."},{"key":"S0022481200067359_ref007","volume-title":"Applications of model theory of degrees of unsolvability","author":"Shoenfield","year":"1963"},{"key":"S0022481200067359_ref001","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.43.2.236"},{"key":"S0022481200067359_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1944-08111-1"},{"key":"S0022481200067359_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1970393"},{"key":"S0022481200067359_ref005","volume-title":"Degrees of unsolvability","author":"Sacks","year":"1963"},{"key":"S0022481200067359_ref003","first-page":"194","article-title":"Negative answer to the problem of reducibility of the theory of algorithms (Russian)","volume":"108","author":"Mu\u010dnik","year":"1956","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200067359_ref002","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200067359","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T20:59:44Z","timestamp":1559509184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200067359\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1966,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1966,6]]}},"alternative-id":["S0022481200067359"],"URL":"https:\/\/doi.org\/10.2307\/2269807","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1966,6]]}}}