{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:39:05Z","timestamp":1775839145940,"version":"3.50.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4119,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is shown that there exists a low<jats:sub>2<\/jats:sub> Harrington non-splitting base \u2014 that is, a low<jats:sub>2<\/jats:sub> computably enumerable (c.e.) degree <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> such that for any c.e. degrees <jats:bold><jats:italic>x, y<\/jats:italic><\/jats:bold>, if <jats:bold><jats:italic>0<\/jats:italic>\u2032<\/jats:bold> = <jats:bold><jats:italic>x<\/jats:italic><\/jats:bold> \u2228 <jats:italic>y<\/jats:italic>, then either <jats:bold><jats:italic>0<\/jats:italic>\u2032<\/jats:bold> = <jats:italic>x<\/jats:italic> \u2228 <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> or <jats:bold><jats:italic>0<\/jats:italic>\u2032<\/jats:bold> = <jats:italic>y<\/jats:italic> \u2228 <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold>. Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the low<jats:sub>2<\/jats:sub>-ness requirements to be satisfied, and the proof given involves new techniques with potentially wider application.<\/jats:p>","DOI":"10.2178\/jsl\/1190150292","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:16:54Z","timestamp":1197573414000},"page":"1391-1430","source":"Crossref","is-referenced-by-count":6,"title":["Splitting and nonsplitting, II: A low<sub>2<\/sub> c.e. degree above which <i>0<\/i>\u2032 is not splittable"],"prefix":"10.1017","volume":"67","author":[{"given":"S. Barry","family":"Cooper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angsheng","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009142_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/1970776"},{"key":"S0022481200009142_ref003","unstructured":"Cooper S. 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