{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T22:42:41Z","timestamp":1775860961047,"version":"3.50.1"},"reference-count":4,"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":16301,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb.\n                        log."],"published-print":{"date-parts":[[1969,7,25]]},"abstract":"<jats:p>In [3] F. P. Ramsey proved as a theorem of Zermelo-Fraenkel set theory (ZF)\n                        with the Axiom of Choice (AC) the following result:<\/jats:p><jats:p>(1) Theorem. <jats:italic>Let A be an infinite class. For each integer n and\n                           partition {X<\/jats:italic>, <jats:italic>Y} of the size n subsets of A, there\n                           exists an infinite subclass of A all of whose size n subsets are\n                           contained in only one of X or Y<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2271095","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:53:51Z","timestamp":1146948831000},"page":"205-206","source":"Crossref","is-referenced-by-count":17,"title":["The independence of Ramsey's theorem"],"prefix":"10.1017","volume":"34","author":[{"given":"E. M.","family":"Kleinberg","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200094445_ref001","volume-title":"Set theory and the continuum hypothesis","author":"Cohen","year":"1966"},{"key":"S0022481200094445_ref002","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.25.4.220"},{"key":"S0022481200094445_ref003","first-page":"264","article-title":"On a problem of formal logic","volume":"30","author":"Ramsey","year":"1929","journal-title":"Proceedings of the London Mathematical Society"},{"key":"S0022481200094445_ref004","first-page":"132","article-title":"The problem of predicatvity","author":"Shoenfield","journal-title":"Essays on the foundations of mathematics"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200094445","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:35:46Z","timestamp":1679466946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200094445\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1969,7,25]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1969,7,25]]}},"alternative-id":["S0022481200094445"],"URL":"https:\/\/doi.org\/10.2307\/2271095","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1969,7,25]]}}}