{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T14:35:50Z","timestamp":1648737350443},"reference-count":7,"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":7224,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1994,6]]},"abstract":"<jats:p>In this paper we investigate the closure of certain filters under different definitions of diagonal intersection. The space of partitions over which filters concern us is <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>\u03ba<\/jats:italic><\/jats:sub>(<jats:italic>\u03bb<\/jats:italic>), the set of partitions of <jats:italic>\u03bb<\/jats:italic> into fewer than <jats:italic>\u03ba<\/jats:italic> pieces, invented by Henle and Zwicker [4] in the spirit of <jats:italic>P<\/jats:italic><jats:sub><jats:italic>\u03ba<\/jats:italic><\/jats:sub>(<jats:italic>\u03bb<\/jats:italic>). Various notions of normality for filters over <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>\u03ba<\/jats:italic><\/jats:sub>(<jats:italic>\u03bb<\/jats:italic>) have been introduced in [4] and [7]. Our objective is to find a notion of normality in terms of a tractable diagonal intersection which also in some sense reflects the construction of a partition. Extending the parallels between <jats:italic>P<\/jats:italic><jats:sub><jats:italic>\u03ba<\/jats:italic><\/jats:sub>(<jats:italic>\u03bb<\/jats:italic>) and <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>\u03ba<\/jats:italic><\/jats:sub>(<jats:italic>\u03bb<\/jats:italic>) we define two diagonal intersections, \u0394<jats:sub>1<\/jats:sub> and \u0394<jats:sub>2<\/jats:sub>, under which the club filter is closed.<\/jats:p>","DOI":"10.2307\/2275405","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:51:53Z","timestamp":1146955913000},"page":"529-533","source":"Crossref","is-referenced-by-count":0,"title":["Normality of a filter over a space of partitions"],"prefix":"10.1017","volume":"59","author":[{"given":"Mark","family":"Fuller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200019952_ref007","first-page":"769","volume":"57","author":"M\u00e9ndez","year":"1992","journal-title":"Filters on the space of partitions Q\n                     \u03ba\n                  (\u03bb)"},{"key":"S0022481200019952_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90009-1"},{"key":"S0022481200019952_ref004","first-page":"137","volume":"47","author":"Henle","year":"1982","journal-title":"Ultrafilters on spaces of partitions"},{"key":"S0022481200019952_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1987-0908659-0"},{"key":"S0022481200019952_ref002","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19900360404"},{"key":"S0022481200019952_ref001","first-page":"316","article-title":"The minimal normal filter in P\n                     \u03ba\n                  (\u03bb)","volume":"86","author":"Carr","year":"1982","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200019952_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90014-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200019952","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T04:00:40Z","timestamp":1557892840000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200019952\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["S0022481200019952"],"URL":"https:\/\/doi.org\/10.2307\/2275405","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}