{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:13:04Z","timestamp":1775463184809,"version":"3.50.1"},"reference-count":10,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2009,11,17]],"date-time":"2009-11-17T00:00:00Z","timestamp":1258416000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that non\u2010isolated from below 2\u2010c.e. <jats:italic>Q<\/jats:italic> \u2010degrees are dense in the structure of c.e. <jats:italic>Q<\/jats:italic> \u2010degrees. We construct a 2\u2010c.e. <jats:italic>Q<\/jats:italic> \u2010degree, which can't be isolated from below not only by c.e. <jats:italic>Q<\/jats:italic> \u2010degrees, but by any <jats:italic>Q<\/jats:italic> \u2010degree. We also prove that below any c.e. <jats:italic>Q<\/jats:italic> \u2010degree there is a 2\u2010c.e. <jats:italic>Q<\/jats:italic> \u2010degree, which is non\u2010isolated from below and from above (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200810026","type":"journal-article","created":{"date-parts":[[2009,11,18]],"date-time":"2009-11-18T00:15:31Z","timestamp":1258503331000},"page":"587-597","source":"Crossref","is-referenced-by-count":3,"title":["Non\u2010isolated quasi\u2010degrees"],"prefix":"10.1002","volume":"55","author":[{"given":"Ilnur I.","family":"Batyrshin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2009,11,17]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"H.Rogers Jr. Theory of Recursive Functions and Effective Computability (McGraw\u2010Hill 1967)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01463347"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00013-X"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1215\/ijm\/1258138538","article-title":"Q\u2010degrees of n\u2010c. e. sets","volume":"51","author":"Arslanov M. M.","year":"2007","journal-title":"Illinois Journal of Mathematics"},{"key":"e_1_2_1_6_2","unstructured":"M. M.Arslanov I. I.Batyrshin andR.Sh. Omanadze Structural properties ofQ\u2010degrees of n\u2010c. e. sets. Annals of Pure and Applied Logic to appear."},{"key":"e_1_2_1_7_2","unstructured":"I. I.Batyrshin Isolated 2\u2010computably enumerableQ\u2010degrees. Izvestiya VUZ. Matematika to appear; Russian Mathematics to appear (English translation)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"R. I.Soare Recursively Enumerable Sets and Degrees (Springer\u2010Verlag Berlin 1987).","DOI":"10.1007\/978-3-662-02460-7"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"M. M.Arslanov S.Lempp andR. A.Shore On isolating r. e. and isolated d\u2010r. e. degrees. In: Computability enumerability unsolvability (S. B. Cooper T. A. Slaman and S. S. Wainer eds.) pp. 61\u201380 (Cambridge University Press 1996).","DOI":"10.1017\/CBO9780511629167.003"},{"key":"e_1_2_1_10_2","first-page":"20","article-title":"Isolated from above d\u2010r. e. degrees, I. Izvestiya VUZ","volume":"2","author":"Efremov S. S.","year":"1998","journal-title":"Matematika"},{"key":"e_1_2_1_11_2","first-page":"18","article-title":"Isolated from above d\u2010r. e. degrees, II. Izvestiya VUZ","volume":"7","author":"Efremov S. 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