{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T10:22:22Z","timestamp":1648549342558},"reference-count":5,"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":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For <jats:italic>X<\/jats:italic> \u2286 <jats:italic>\u03c9<\/jats:italic>, let [<jats:italic>X<\/jats:italic>]<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> denote the class of all <jats:italic>n<\/jats:italic>-element subsets of <jats:italic>X<\/jats:italic>. An infinite set <jats:italic>A<\/jats:italic> \u2286 <jats:italic>\u03c9<\/jats:italic> is called <jats:italic>n<\/jats:italic>-r-<jats:italic>cohesive<\/jats:italic> if for each computable function <jats:italic>f<\/jats:italic>: [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> \u2192 {0, 1} there is a finite set <jats:italic>F<\/jats:italic> such that <jats:italic>f<\/jats:italic> is constant on [<jats:italic>A \u2212 F<\/jats:italic>]<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>. We show that for each <jats:italic>n<\/jats:italic> &gt; 2 there is no \u03a0<jats:sub arrange=\"stack\"><jats:italic>n<\/jats:italic><\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> set <jats:italic>A<\/jats:italic> \u2286 <jats:italic>\u03c9<\/jats:italic> which is <jats:italic>n<\/jats:italic>-r-<jats:italic>cohesive<\/jats:italic>. For <jats:italic>n<\/jats:italic> = 2 this refutes a result previously claimed by the authors, and for <jats:italic>n<\/jats:italic> \u2265 3 it answers a question raised by the authors.<\/jats:p>","DOI":"10.2178\/jsl\/1190150150","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:14:26Z","timestamp":1197573266000},"page":"1078-1082","source":"Crossref","is-referenced-by-count":0,"title":["Generalized r-cohesiveness and the arithmetical hierarchy: a correction to \u201cGeneralized cohesiveness\u201d"],"prefix":"10.1017","volume":"67","author":[{"suffix":"Jr.","given":"Carl G.","family":"Jockusch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamara J.","family":"Lakins","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009439_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200009439_ref004","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"S0022481200009439_ref001","first-page":"489","volume":"64","author":"Hummel","year":"1999","journal-title":"Generalized cohesiveness"},{"key":"S0022481200009439_ref002","first-page":"873","volume":"66","author":"Hummel","year":"2001","journal-title":"Ramsey's theorem for computably enumerable colorings"},{"key":"S0022481200009439_ref003","first-page":"268","volume":"37","author":"Jockusch","year":"1972","journal-title":"Ramsey's theorem and recursion theory"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:45:58Z","timestamp":1557189958000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009439\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009439"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150150","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}