{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T05:20:47Z","timestamp":1774588847543,"version":"3.50.1"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Say that (<jats:bold><jats:italic>a, d<\/jats:italic><\/jats:bold>) is an isolation pair if <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> is a c.e. degree, <jats:bold><jats:italic>d<\/jats:italic><\/jats:bold> is a d.c.e. degree, <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> &lt; <jats:bold><jats:italic>d<\/jats:italic><\/jats:bold> and <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> bounds all c.e. degrees below <jats:bold><jats:italic>d<\/jats:italic><\/jats:bold>. We prove that there are an isolation pair (<jats:bold><jats:italic>a, d<\/jats:italic><\/jats:bold>) and a c.e. degree <jats:bold><jats:italic>c<\/jats:italic><\/jats:bold> such that <jats:bold><jats:italic>c<\/jats:italic><\/jats:bold> is incomparable with <jats:bold><jats:italic>a, d<\/jats:italic><\/jats:bold>, and <jats:bold><jats:italic>c<\/jats:italic><\/jats:bold> cups <jats:bold><jats:italic>d<\/jats:italic><\/jats:bold> to <jats:bold><jats:italic>o<\/jats:italic><\/jats:bold>\u2032, caps <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> to <jats:bold><jats:italic>o<\/jats:italic><\/jats:bold>. Thus, {<jats:bold><jats:italic>o, c, d, o<\/jats:italic><\/jats:bold>\u2032} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of <jats:italic>N<\/jats:italic><jats:sub>5<\/jats:sub> embedding.<\/jats:p>","DOI":"10.2178\/jsl\/1190150148","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:14:26Z","timestamp":1197573266000},"page":"1055-1064","source":"Crossref","is-referenced-by-count":12,"title":["Isolation and lattice embeddings"],"prefix":"10.1017","volume":"67","author":[{"given":"Guohua","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009415_ref011","volume-title":"Archive for Mathematical Logic","author":"Ishmukhametov"},{"key":"S0022481200009415_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200009415_ref003","unstructured":"Cooper S. B. , Degrees of unsolvability, Ph.D. thesis, Leicester University, Leicester, England."},{"key":"S0022481200009415_ref001","first-page":"270","article-title":"Structural properties of the degrees below o\u2032","volume":"283","author":"Arslanov","year":"1985","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200009415_ref013","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611599011818"},{"key":"S0022481200009415_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9754-0_4"},{"key":"S0022481200009415_ref008","doi-asserted-by":"publisher","DOI":"10.1142\/9789812812940_0005"},{"key":"S0022481200009415_ref002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629167.003"},{"key":"S0022481200009415_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02937291"},{"key":"S0022481200009415_ref006","unstructured":"Cooper S. B. and Yi X. , Isolated d.c.e. degrees, Preprint series, no. 17, p. 25, Preprint series, no. 17, University of Leeds, Department of Pure Mathematics, 1995, p. 25."},{"key":"S0022481200009415_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050053"},{"key":"S0022481200009415_ref009","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/21.1.43"},{"key":"S0022481200009415_ref012","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420108"},{"key":"S0022481200009415_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90005-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009415","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:45:31Z","timestamp":1557189931000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009415\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009415"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150148","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}