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Ramsey [14]:<\/jats:p><jats:p>Theorem 0.1. <jats:italic>Let n be a positive integer and let<\/jats:italic> {A, B} <jats:italic>be a partition of those subsets of the nonnegative integers containing exactly n elements. Then there exists an infinite subset x of the nonnegative integers all of whose n-element subsets are contained in only one of A or B. (Any such set x is said to be \u201chomogeneous\u201d for the partition.)<\/jats:italic><\/jats:p>","DOI":"10.2307\/2270698","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:02:31Z","timestamp":1146949351000},"page":"410-428","source":"Crossref","is-referenced-by-count":24,"title":["Strong partition properties for infinite cardinals"],"prefix":"10.1017","volume":"35","author":[{"given":"E. M.","family":"Kleinberg","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200090113_ref016","volume-title":"Some applications of model theory in set theory","author":"Silver","year":"1966"},{"key":"S0022481200090113_ref015","unstructured":"Rowbottom F. , Large cardinals and constructible sets, Doctoral dissertation, University of Wisconsin, Madison, Wis., 1964."},{"key":"S0022481200090113_ref014","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"S0022481200090113_ref013","unstructured":"Morley M. , Categoricity in power, Doctoral dissertation, University of Chicago, Chicago, Ill., 1962."},{"key":"S0022481200090113_ref010","first-page":"840","article-title":"Somewhat homogeneous sets","volume":"16","author":"Kleinberg","year":"1969","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200090113_ref008","first-page":"579","article-title":"Strong partition properties","volume":"16","author":"Kleinberg","year":"1969","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200090113_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1956-10036-0"},{"key":"S0022481200090113_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01886396"},{"key":"S0022481200090113_ref007","first-page":"253","article-title":"Ramsey cardinals and the general continuum hypothesis","volume":"14","author":"Jensen","year":"1967","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200090113_ref006","first-page":"548","article-title":"A generalization of Ramsey's theorem","volume":"15","author":"Galvin","year":"1968","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200090113_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02023868"},{"key":"S0022481200090113_ref004","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.417"},{"key":"S0022481200090113_ref011","unstructured":"Martin D. 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