{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T16:25:43Z","timestamp":1767198343767,"version":"build-2238731810"},"reference-count":21,"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":9415,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1988,6]]},"abstract":"<jats:p>\n                    <jats:bold>\u00a70. Introduction.<\/jats:bold>\n                    We started our study of filters of partitions in [15]. We shall here restrict ourselves to the consideration of filters on (\u03c9)\n                    <jats:sup>\u03c9<\/jats:sup>\n                    , the set of all infinite partitions of \u03c9. \u00a71 is an attempt to elucidate the connection between filters on (\u03c9)\n                    <jats:sup>\u03c9<\/jats:sup>\n                    and filters over \u03c9. Given a filter\n                    <jats:italic>H<\/jats:italic>\n                    over \u03c9, we define two filters\n                    <jats:italic>\n                      F\n                      <jats:sub>H<\/jats:sub>\n                    <\/jats:italic>\n                    and\n                    <jats:italic>\n                      G\n                      <jats:sub>H<\/jats:sub>\n                    <\/jats:italic>\n                    on (\u03c9)\n                    <jats:sup>\u03c9<\/jats:sup>\n                    , and we characterize\n                    <jats:italic>p<\/jats:italic>\n                    -points, rare ultrafilters and Ramsey ultrafilters in terms of properties of the associated filters of partitions.\n                  <\/jats:p>\n                  <jats:p>\n                    The remainder of the paper is devoted to the study of those filters that can be associated with Hindman's theorem and its extensions. Let us introduce some notation. Suppose * is an associative operation on \u03c9, and let a subset\n                    <jats:italic>A<\/jats:italic>\n                    of \u03c9 and an ordinal \u03b1 with 0 &lt; \u03b1 \u2264 \u03c9 be given.\n                  <\/jats:p>","DOI":"10.2307\/2274523","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:25:43Z","timestamp":1146939943000},"page":"540-553","source":"Crossref","is-referenced-by-count":10,"title":["Some filters of partitions"],"prefix":"10.1017","volume":"53","author":[{"given":"Pierre","family":"Matet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200028450_bib019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21543-2"},{"key":"S0022481200028450_bib016","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90006-7"},{"key":"S0022481200028450_bib002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1987-0906807-4"},{"key":"S0022481200028450_bib008","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(74)90023-5"},{"key":"S0022481200028450_bib007","first-page":"341","article-title":"The existence of certain ultrafilters on N and a conjecture of Graham and Rothschild","volume":"36","author":"Hindman","year":"1972","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200028450_bib017","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(75)90039-4"},{"key":"S0022481200028450_bib015","first-page":"12","volume":"51","author":"Matet","year":"1986","journal-title":"Partitions and filters"},{"key":"S0022481200028450_bib005","first-page":"143","article-title":"Deux classes remarquables d'ultrafiltres sur N","volume":"92","author":"Choquet","year":"1968","journal-title":"Bulletin des Sciences Math\u00e9matiques"},{"key":"S0022481200028450_bib010","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/065\/891252"},{"key":"S0022481200028450_bib006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1977-14316-4"},{"key":"S0022481200028450_bib021","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(76)90058-3"},{"key":"S0022481200028450_bib014","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90009-4"},{"key":"S0022481200028450_bib011","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200028450_bib013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02756789"},{"key":"S0022481200028450_bib018","volume-title":"S\u00e9minaire de th\u00e9orie du potentiel","author":"Mokobodzki","year":"1967"},{"key":"S0022481200028450_bib004","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(84)90026-4"},{"key":"S0022481200028450_bib003","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90005-7"},{"key":"S0022481200028450_bib020","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(85)90003-X"},{"key":"S0022481200028450_bib012","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100053032"},{"key":"S0022481200028450_bib001","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/065\/891244"},{"key":"S0022481200028450_bib009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062706"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200028450","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:37:15Z","timestamp":1679467035000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200028450\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,6]]},"references-count":21,"aliases":["10.1017\/s0022481200028450"],"journal-issue":{"issue":"2","published-print":{"date-parts":[[1988,6]]}},"alternative-id":["S0022481200028450"],"URL":"https:\/\/doi.org\/10.2307\/2274523","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,6]]}}}