{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T15:05:59Z","timestamp":1780499159086,"version":"3.54.1"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1745,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low<jats:sub>2<\/jats:sub> homogeneous set <jats:italic>H<\/jats:italic>. We answer a question of the same authors by showing that <jats:italic>H<\/jats:italic> may be chosen to satisfy in addition <jats:italic>C<\/jats:italic> \u2270<jats:sub>r<\/jats:sub><jats:italic>H<\/jats:italic>, where <jats:italic>C<\/jats:italic> is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable 2-coloring of pairs admits a pair of low<jats:sub>2<\/jats:sub> infinite homogeneous sets whose degrees form a minimal pair.<\/jats:p>","DOI":"10.2178\/jsl\/1243948327","type":"journal-article","created":{"date-parts":[[2009,6,2]],"date-time":"2009-06-02T13:12:25Z","timestamp":1243948345000},"page":"557-578","source":"Crossref","is-referenced-by-count":26,"title":["Ramsey's theorem and cone avoidance"],"prefix":"10.1017","volume":"74","author":[{"given":"Damir D.","family":"Dzhafarov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"suffix":"Jr.","given":"Carl G.","family":"Jockusch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000356X_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390153"},{"key":"S002248120000356X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0016275"},{"key":"S002248120000356X_ref006","first-page":"33","article-title":"\u03a010 classes and degrees of theories","volume":"173","author":"Jockusch","year":"1972","journal-title":"Transactions of the American Mathematical Society"},{"key":"S002248120000356X_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71117-0"},{"key":"S002248120000356X_ref009","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1305\/ndjfl\/1040136917","article-title":"On the strength of Ramsey's theorem","volume":"36","author":"Seetapun","year":"1995","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S002248120000356X_ref003","first-page":"1301","volume":"59","author":"Hummel","year":"1994","journal-title":"Effective versions of Ramsey's theorem: avoiding the cone above 0\u2032"},{"key":"S002248120000356X_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S002248120000356X_ref001","first-page":"1","volume":"66","author":"Cholak","year":"2001","journal-title":"On the strength of Ramsey's theorem for pairs"},{"key":"S002248120000356X_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S002248120000356X_ref004","first-page":"268","volume":"37","author":"Jockusch","year":"1972","journal-title":"Ramsey's theorem and recursion theory"},{"key":"S002248120000356X_ref005","first-page":"1288","volume":"54","author":"Jockusch","year":"1989","journal-title":"Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion"},{"key":"S002248120000356X_ref002","doi-asserted-by":"publisher","DOI":"10.1142\/9789812796554_0008"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000356X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T13:26:06Z","timestamp":1556630766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000356X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["S002248120000356X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1243948327","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}