{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T07:11:45Z","timestamp":1769238705433,"version":"3.49.0"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":10238,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1986,3]]},"abstract":"<jats:p>In [2], Carlson and Simpson proved a dualized version of Ramsey's theorem obtained by coloring partitions of <jats:italic>\u03c9<\/jats:italic> instead of subsets of <jats:italic>\u03c9<\/jats:italic>. It was at the suggestion of Simpson that the author undertook to study the notion dual to that of a Ramsey ultrafilter. After stating the basic terminology and notation used in the paper in \u00a71, in \u00a72 we establish some basic properties of the lattice of all partitions of a cardinal <jats:italic>\u03ba<\/jats:italic>. \u00a73 is devoted to the study of families of pairwise disjoint partitions of <jats:italic>\u03c9<\/jats:italic>. \u00a74 is concerned with descending sequences of partitions. In \u00a75, we give some examples of filters of partitions. Properties of such filters are discussed in \u00a76. Co-Ramsey filters are introduced in \u00a77, and it is shown how they can be associated with Ramsey ultrafilters. The main result of \u00a78 is Proposition 8.1, which asserts the existence of a co-Ramsey filter under the continuum hypothesis.<\/jats:p><jats:p>We use standard set theoretic conventions and notation. Let <jats:italic>\u03ba<\/jats:italic> be a cardinal. We set <jats:italic>\u03ba<\/jats:italic>* = <jats:italic>\u03ba<\/jats:italic> \u2212 {0}. For every ordinal <jats:italic>\u03b1<\/jats:italic> \u2264 <jats:italic>\u03ba<\/jats:italic>, (<jats:italic>\u03ba<\/jats:italic>)<jats:italic><jats:sup>\u03b1<\/jats:sup><\/jats:italic> denotes the set of those sequences <jats:italic>X<\/jats:italic>(<jats:italic>\u03bd<\/jats:italic>), <jats:italic>\u03bd<\/jats:italic> &lt; <jats:italic>\u03b1<\/jats:italic>, of pairwise disjoint nonempty subsets of <jats:italic>\u03ba<\/jats:italic> such that \u22c3<jats:sub><jats:italic>\u03bd<\/jats:italic>&lt;<jats:italic>\u03b1<\/jats:italic><\/jats:sub><jats:italic>X<\/jats:italic>(<jats:italic>\u03bd<\/jats:italic>) = <jats:italic>\u03ba<\/jats:italic>, and \u22c2<jats:italic>X<\/jats:italic>(<jats:italic>\u03bd<\/jats:italic>) &lt; \u22c2<jats:italic>X<\/jats:italic>(<jats:italic>\u03bd<\/jats:italic>\u2032) whenever <jats:italic>\u03bd<\/jats:italic> &lt; <jats:italic>\u03bd<\/jats:italic>\u2032. We also let (<jats:italic>\u03ba<\/jats:italic>)<jats:sup>\u2264<jats:italic>\u03b1<\/jats:italic><\/jats:sup> = \u22c3<jats:sub><jats:italic>\u03b2<\/jats:italic>\u2264<jats:italic>\u03b1<\/jats:italic><\/jats:sub>(<jats:italic>\u03ba<\/jats:italic>)<jats:sup><jats:italic>\u03b2<\/jats:italic><\/jats:sup> and (<jats:italic>\u03ba<\/jats:italic>)<jats:sup>&lt;<jats:italic>\u03b1<\/jats:italic><\/jats:sup> = \u22c3<jats:sub><jats:italic>\u03b2<\/jats:italic>&lt;<jats:italic>\u03b1<\/jats:italic><\/jats:sub>(<jats:italic>\u03ba<\/jats:italic>)<jats:sup><jats:italic>\u03b2<\/jats:italic><\/jats:sup>. Given <jats:italic>X<\/jats:italic> \u2208 (<jats:italic>\u03ba<\/jats:italic>)<jats:sup><jats:italic>\u03b1<\/jats:italic><\/jats:sup>, we put <jats:italic>x<\/jats:italic><jats:sub><jats:italic>\u03bd<\/jats:italic><\/jats:sub> = \u22c2<jats:italic>X<\/jats:italic>(<jats:italic>\u03bd<\/jats:italic>) for every <jats:italic>\u03bd<\/jats:italic> &lt; <jats:italic>\u03b1<\/jats:italic>, and we denote by <jats:italic>A<jats:sub>x<\/jats:sub><\/jats:italic> the set of all <jats:italic>x<\/jats:italic><jats:sub><jats:italic>\u03bd<\/jats:italic><\/jats:sub>, 0 &lt; <jats:italic>\u03bd<\/jats:italic> &lt; <jats:italic>\u03b1<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273937","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:16:32Z","timestamp":1146939392000},"page":"12-21","source":"Crossref","is-referenced-by-count":15,"title":["Partitions and filters"],"prefix":"10.1017","volume":"51","author":[{"given":"P.","family":"Matet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200031492_ref003","first-page":"193","volume":"38","author":"Galvin","year":"1973","journal-title":"Borel sets and Ramsey's theorem"},{"key":"S0022481200031492_ref004","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200031492_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90006-7"},{"key":"S0022481200031492_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90005-7"},{"key":"S0022481200031492_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90009-4"},{"key":"S0022481200031492_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(84)90026-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200031492","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T03:34:42Z","timestamp":1558496082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200031492\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,3]]}},"alternative-id":["S0022481200031492"],"URL":"https:\/\/doi.org\/10.2307\/2273937","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,3]]}}}