{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T06:37:04Z","timestamp":1759991824080},"reference-count":3,"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":4575,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct the set of the title, answering a question of Cholak, Jockusch. and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every <jats:italic>\u03c9<\/jats:italic>-model of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200010690_inline1\" \/> must contain a nonlow set.<\/jats:p>","DOI":"10.2307\/2695113","type":"journal-article","created":{"date-parts":[[2006,11,22]],"date-time":"2006-11-22T22:25:31Z","timestamp":1164234331000},"page":"1371-1381","source":"Crossref","is-referenced-by-count":19,"title":["A \u0394<sub>2<\/sub><sup>0<\/sup> set with no infinite low subset in either it or its complement"],"prefix":"10.1017","volume":"66","author":[{"given":"Rod","family":"Downey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis R.","family":"Hirschfeldt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steffen","family":"Lempp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reed","family":"Solomon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200010690_ref001","unstructured":"Cholak P. A. , Jockusch C. G. Jr. , and Slaman T. A. , On the strength of Ramsey's theorem for pairs, to appear in this journal."},{"key":"S0022481200010690_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S0022481200010690_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200010690","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T23:26:21Z","timestamp":1557271581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200010690\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,9]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,9]]}},"alternative-id":["S0022481200010690"],"URL":"https:\/\/doi.org\/10.2307\/2695113","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,9]]}}}