{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T18:56:32Z","timestamp":1649184992230},"reference-count":16,"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":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define a property <jats:italic>R<\/jats:italic>(<jats:italic>A<\/jats:italic><jats:sub>0<\/jats:sub>, <jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub>) in the partial order <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009683_inline1\" \/> of computably enumerable sets under inclusion, and prove that <jats:italic>R<\/jats:italic> implies that <jats:italic>A<\/jats:italic><jats:sub>0<\/jats:sub> is noncomputable and incomplete. Moreover, the property is nonvacuous. and the <jats:italic>A<\/jats:italic><jats:sub>0<\/jats:sub> and <jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub> which we build satisfying <jats:italic>R<\/jats:italic> form a Friedberg splitting of their union <jats:italic>A<\/jats:italic>, with <jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub> prompt and <jats:italic>A<\/jats:italic> promptly simple. We conclude that <jats:italic>A<\/jats:italic><jats:sub>0<\/jats:sub> and <jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub> lie in distinct orbits under automorphisms of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009683_inline1\" \/>, yielding a strong answer to a question previously explored by Downey, Stob, and Soare about whether halves of Friedberg splittings must lie in the same orbit.<\/jats:p>","DOI":"10.2178\/jsl\/1190150104","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:13:31Z","timestamp":1197573211000},"page":"679-696","source":"Crossref","is-referenced-by-count":0,"title":["Definable incompleteness and Friedberg splittings"],"prefix":"10.1017","volume":"67","author":[{"given":"Russell","family":"Miller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009683_ref007","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.88.22.10242"},{"key":"S0022481200009683_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90031-3"},{"key":"S0022481200009683_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19910370802"},{"key":"S0022481200009683_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00069-9"},{"key":"S0022481200009683_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1097164-6"},{"key":"S0022481200009683_ref011","first-page":"193","volume":"36","author":"Lerman","year":"1971","journal-title":"Some theorems on r-maximal sets and major subsets of recursively enumerable sets"},{"key":"S0022481200009683_ref013","first-page":"194","article-title":"On the unsolvability of the problem of reducibilily in the theory of algorithms","volume":"109","author":"Muchnik","year":"1956","journal-title":"Dokl. Akad. Nauk SSSR, N. S."},{"key":"S0022481200009683_ref014","first-page":"220","volume":"21","author":"Myhill","year":"1956","journal-title":"The lattice of recursively enumerable sets"},{"key":"S0022481200009683_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0541"},{"key":"S0022481200009683_ref015","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1987"},{"key":"S0022481200009683_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(92)90065-S"},{"key":"S0022481200009683_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90092-R"},{"key":"S0022481200009683_ref006","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.43.2.236"},{"key":"S0022481200009683_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00181-6"},{"key":"S0022481200009683_ref010","article-title":"Review of Lerman [11]","volume":"45","author":"Jockusch","year":"1973","journal-title":"Mathematical Reviews"},{"key":"S0022481200009683_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009683","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:05:58Z","timestamp":1557191158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009683\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009683"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150104","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}