{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T09:28:18Z","timestamp":1773221298393,"version":"3.50.1"},"reference-count":24,"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":3388,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>We show that if <jats:bold>d<\/jats:bold> \u2208 <jats:bold>GH<\/jats:bold><jats:sub>1<\/jats:sub> then <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200007477_inline1\"\/>(\u2264 <jats:bold>d<\/jats:bold>) has the complementation property, i.e., for all <jats:bold>a<\/jats:bold> &lt; <jats:bold>d<\/jats:bold> there is some <jats:bold>b<\/jats:bold> &lt; <jats:bold>d<\/jats:bold> such that <jats:bold>a<\/jats:bold> \u2227 <jats:bold>b<\/jats:bold> = <jats:bold>0<\/jats:bold> and <jats:bold>a<\/jats:bold> \u2228 <jats:bold>b<\/jats:bold> = <jats:bold>d<\/jats:bold>.<\/jats:p>","DOI":"10.2178\/jsl\/1102022219","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T16:51:32Z","timestamp":1109782292000},"page":"1200-1220","source":"Crossref","is-referenced-by-count":6,"title":["Generalized high degrees have the complementation property"],"prefix":"10.1017","volume":"69","author":[{"given":"Noam","family":"Greenberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Montalb\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard A.","family":"Shore","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007477_ref023","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.1999.v6.n6.a10"},{"key":"S0022481200007477_ref022","first-page":"571\u2013574","volume":"39","author":"Sasso","year":"1974","journal-title":"A minimal degree not realizing least possible jump"},{"key":"S0022481200007477_ref021","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1961-10652-6"},{"key":"S0022481200007477_ref020","first-page":"A\u2013615","article-title":"Degrees joining 0\u2032","volume":"19","author":"Robinson","year":"1972","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200007477_ref017","unstructured":"Posner D. 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