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More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees<jats:bold>f<\/jats:bold>&gt;<jats:bold>e<\/jats:bold>&gt;<jats:bold>d<\/jats:bold>&gt;<jats:bold>0<\/jats:bold>such that any degree<jats:bold>u<\/jats:bold>\u2264<jats:bold>f<\/jats:bold>is either comparable with both<jats:bold>e<\/jats:bold>and<jats:bold>d<\/jats:bold>, or incomparable with both.<\/jats:p>","DOI":"10.2178\/jsl\/1268917488","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"401-441","source":"Crossref","is-referenced-by-count":18,"title":["On Downey's conjecture"],"prefix":"10.1017","volume":"75","author":[{"given":"Marat M.","family":"Arslanov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iskander Sh.","family":"Kalimullin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steffen","family":"Lempp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002619_ref007","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/21.1.43"},{"key":"S0022481200002619_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1961-10652-6"},{"key":"S0022481200002619_ref013","first-page":"49","volume":"30","author":"Putnam","year":"1965","journal-title":"Trial and error predicates and the solution to a problem of Mostowski"},{"key":"S0022481200002619_ref011","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-16.1.537"},{"key":"S0022481200002619_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02937291"},{"key":"S0022481200002619_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/1970393"},{"key":"S0022481200002619_ref002","volume-title":"Computability theory and its applications (Boulder, CO, 1999)","author":"Arslanov","year":"2000"},{"key":"S0022481200002619_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90005-7"},{"key":"S0022481200002619_ref001","first-page":"27","volume-title":"Izvestiya Vysshikh Uchebnykh Zavedeni\u012d. 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Leicester University, Leicester, England, 1971,"},{"key":"S0022481200002619_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200002619_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02219847"},{"key":"S0022481200002619_ref012","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1007\/BFb0090950","volume-title":"Logic Year 1979\u201380 (Proceedings of the Seminars and Conference on Mathematical Logic, University of Connecticut, Storrs, Connecticut, 1979\/80)","author":"Miller","year":"1981"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002619","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:04:42Z","timestamp":1591157082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002619\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["S0022481200002619"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1268917488","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}