{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T15:13:15Z","timestamp":1648998795950},"reference-count":18,"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":1107,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that for every \u03a3<jats:sub arrange=\"stack\">2<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> enumeration degree <jats:italic>b<\/jats:italic> there exists a noncuppable \u03a3<jats:sub arrange=\"stack\">2<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> degree <jats:italic>a<\/jats:italic> &gt; 0<jats:sub>e<\/jats:sub> such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002036_inline1\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002036_inline2\" \/>. This allows us to deduce, from results on the high\/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002036_inline3\" \/>, that there exist \u03a3<jats:sub arrange=\"stack\">2<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> noncuppable enumeration degrees at every possible\u2014i.e., above low<jats:sub>1<\/jats:sub>\u2014level of the high\/low jump hierarchy in the context of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002036_inline4\" \/>.<\/jats:p>","DOI":"10.2178\/jsl\/1294170994","type":"journal-article","created":{"date-parts":[[2011,1,4]],"date-time":"2011-01-04T15:22:35Z","timestamp":1294154555000},"page":"177-197","source":"Crossref","is-referenced-by-count":2,"title":["On the jump classes of noncuppable enumeration degrees"],"prefix":"10.1017","volume":"76","author":[{"given":"Charles M.","family":"Harris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002036_ref016","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1967-0207558-7"},{"key":"S0022481200002036_ref009","article-title":"Noncuppable enumeration degrees via finite injury","author":"Harris","journal-title":"Journal of Logic and Computation"},{"key":"S0022481200002036_ref014","volume-title":"Classical recursion theory","author":"Odifreddi","year":"1989"},{"key":"S0022481200002036_ref013","first-page":"285","volume":"65","author":"Nies","year":"2000","journal-title":"Structural properties and \u03a320 enumeration degrees"},{"key":"S0022481200002036_ref012","unstructured":"McEvoy K. , The structure of the enumeration degrees, Ph.D. thesis, The University of Leeds, UK, 10 1984."},{"key":"S0022481200002036_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1963-0155747-3"},{"key":"S0022481200002036_ref006","first-page":"1125","volume":"71","author":"Giorgi","year":"2006","journal-title":"Properly \u03a320 enumeration degrees and the high\/low hierarchy"},{"key":"S0022481200002036_ref018","first-page":"303","volume-title":"Complexity, logic and recursion theory","author":"Sorbi","year":"1997"},{"key":"S0022481200002036_ref001","first-page":"57","volume-title":"Recursion theory week, Oberwolfach 1989","volume":"1432","author":"Cooper","year":"1990"},{"key":"S0022481200002036_ref002","volume-title":"Computability theory","author":"Cooper","year":"2004"},{"key":"S0022481200002036_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(96)00009-7"},{"key":"S0022481200002036_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-002-0161-z"},{"key":"S0022481200002036_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0192-9"},{"key":"S0022481200002036_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0220595-7"},{"key":"S0022481200002036_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794984"},{"key":"S0022481200002036_ref003","first-page":"983","volume":"50","author":"Cooper","year":"1985","journal-title":"On minimal pairs of enumeration degrees"},{"key":"S0022481200002036_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200002036_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-006-0021-3"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T15:24:01Z","timestamp":1556378641000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002036\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["S0022481200002036"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1294170994","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}