{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:51:35Z","timestamp":1777517495511,"version":"3.51.4"},"reference-count":21,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T00:00:00Z","timestamp":1594857600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2021,4,16]]},"abstract":"<jats:p>We prove the following result: there is a family [Formula: see text] of subsets of \u03c9 such that for every stable coloring [Formula: see text] hyperarithmetical in R and every finite collection of Turing functionals, there is an infinite homogeneous set H for c such that none of the finitely many functionals map [Formula: see text] to an infinite cohesive set for R. This provides a partial answer to a question in computable combinatorics, whether [Formula: see text] is omnisciently computably reducible to [Formula: see text].<\/jats:p>","DOI":"10.3233\/com-190261","type":"journal-article","created":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T10:30:41Z","timestamp":1594895441000},"page":"111-121","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["COH, SRT22, and multiple functionals"],"prefix":"10.1177","volume":"10","author":[{"given":"Damir D.","family":"Dzhafarov","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Connecticut, CT, U.S.A.."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludovic","family":"Patey","sequence":"additional","affiliation":[{"name":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1, France."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,7,16]]},"reference":[{"key":"ref001","unstructured":"V.\u00a0Brattka, G.\u00a0Gherardi and A.\u00a0Pauly, Weihrauch complexity in computable analysis. to appear."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2017.43"},{"key":"ref003","unstructured":"P.\u00a0Cholak, D.D.\u00a0Dzhafarov, D.R.\u00a0Hirschfeldt and L.\u00a0Patey, Some results concerning the SRT22 vs. COH problem, submitted."},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2694910"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-09-10115-6"},{"key":"ref006","unstructured":"Denis and R.\u00a0Hirschfeldt, Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore. World Scientific Publishing Company Incorporated, 2014."},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6465"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2014-12261-1"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2016.1"},{"key":"ref010","unstructured":"D.D.\u00a0Dzhafarov, J.\u00a0Le Goh, D.R.\u00a0Hirschfeldt, L.\u00a0Patey and A.\u00a0Pauly, Ramsey\u2019s theorem and products in the Weihrauch degrees,\n                      Computability\n                      , to appear."},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/13315"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061316500021"},{"key":"ref013","unstructured":"J.L.\u00a0Hirst and C.\u00a0Mummert, Using Ramsey\u2019s theorem once, to appear."},{"key":"ref014","unstructured":"B.\u00a0Monin and L.\u00a0Patey, \u03a010 encodability and omniscient reductions,\n                      Notre Dame Journal of Formal Logic\n                      , to appear."},{"key":"ref015","unstructured":"B.\u00a0Monin and L.\u00a0Patey, SRT22 does not imply COH in\n                      \u03c9\n                      -models, to appear."},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40189-8_36"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-016-1433-3"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12013-2"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1142\/9789814699952_0002"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31933-4"}],"container-title":["Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-190261","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/COM-190261","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-190261","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:02:49Z","timestamp":1777392169000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-190261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,16]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,4,16]]}},"alternative-id":["10.3233\/COM-190261"],"URL":"https:\/\/doi.org\/10.3233\/com-190261","relation":{},"ISSN":["2211-3568","2211-3576"],"issn-type":[{"value":"2211-3568","type":"print"},{"value":"2211-3576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,16]]}}}