{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T17:23:42Z","timestamp":1769016222375,"version":"3.49.0"},"reference-count":26,"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":3571,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees <jats:bold>c<\/jats:bold><jats:sub>1<\/jats:sub> &lt; <jats:bold>c<\/jats:bold><jats:sub>2<\/jats:sub> and a d.c.e. degree <jats:bold>d<\/jats:bold> \u2208 (<jats:bold>c<\/jats:bold><jats:sub>1<\/jats:sub>, <jats:bold>c<\/jats:bold><jats:sub>2<\/jats:sub>) such that (<jats:bold>c<\/jats:bold><jats:sub>1<\/jats:sub>, <jats:bold>d<\/jats:bold>) and (<jats:bold>d<\/jats:bold>, <jats:bold>c<\/jats:bold><jats:sub>2<\/jats:sub>) contain no c.e. degrees. Thus, the c.e. degrees between <jats:bold>c<\/jats:bold><jats:sub>1<\/jats:sub> and <jats:bold>c<\/jats:bold><jats:sub>2<\/jats:sub> are all incomparable with <jats:bold>d<\/jats:bold>. We also show that there are d.c.e. degrees <jats:bold>d<\/jats:bold><jats:sub>1<\/jats:sub> &lt; <jats:bold>d<\/jats:bold><jats:sub>2<\/jats:sub> such that (<jats:bold>d<\/jats:bold><jats:sub>1<\/jats:sub>, <jats:bold>d<\/jats:bold><jats:sub>2<\/jats:sub>) contains a unique c.e. degree.<\/jats:p>","DOI":"10.2178\/jsl\/1082418534","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:35:02Z","timestamp":1109799302000},"page":"409-420","source":"Crossref","is-referenced-by-count":4,"title":["Bi-isolation in the d.c.e. degrees"],"prefix":"10.1017","volume":"69","author":[{"given":"Guohua","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007817_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9754-0_4"},{"key":"S0022481200007817_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90005-7"},{"key":"S0022481200007817_ref004","first-page":"461","article-title":"A splitting theorem of the n-r.e. degrees","volume":"115","author":"Cooper","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200007817_ref013","first-page":"18","article-title":"Upper isolated d.c.e. degrees","volume":"42","author":"Efremov","year":"1998","journal-title":"II, Izvestiya Vysshikh Uchebnykh Zavedeni\u012d, Matematika"},{"key":"S0022481200007817_ref002","unstructured":"Arslanov M. 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