{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:36:44Z","timestamp":1760121404915},"reference-count":14,"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":8777,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that every analytic filter is generated by a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline1\" \/> prefilter, every <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline2\" \/> filter is generated by a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline3\" \/> prefilter, and if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline4\" \/> is a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline2\" \/> prefilter then the filter generated by it is also <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline2\" \/>. The last result is unique for the Borel classes, as there is a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline1\" \/>-complete prefilter <jats:italic>P<\/jats:italic> such that the filter generated by it is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026591_inline5\" \/>-complete. Also, no complete coanalytic filter is generated by an analytic prefilter. The proofs use K\u00f6nig's infinity lemma, a normal form theorem for monotone analytic sets, and Wadge reductions.<\/jats:p>","DOI":"10.2307\/2274970","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:33:48Z","timestamp":1146940428000},"page":"315-322","source":"Crossref","is-referenced-by-count":4,"title":["On analytic filters and prefilters"],"prefix":"10.1017","volume":"55","author":[{"given":"Samy","family":"Zafrany","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026591_ref007","first-page":"263","article-title":"The structure of \u03c3-ideals of compact sets","volume":"301","author":"Kechris","year":"1987","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200026591_ref003","first-page":"774","volume":"49","author":"Cenzer","year":"1984","journal-title":"Monotone reducibility and the family of infinite sets"},{"key":"S0022481200026591_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1988-0943302-1"},{"key":"S0022481200026591_ref008","volume-title":"Topology","volume":"1","author":"Kuratowski","year":"1966"},{"key":"S0022481200026591_ref013","unstructured":"Zafrany Samy [1987], Complexity of Borel ideals, iterated Fr\u00e9chet quantifiers, and related sets of countable models, Ph.D. thesis, University of California, Berkeley, California."},{"key":"S0022481200026591_ref012","unstructured":"Wadge William Wilfred [1983], Reducibility and determinateness on the Baire space, Ph.D. thesis, University of California, Berkeley, California."},{"key":"S0022481200026591_ref001","first-page":"759","article-title":"Classes de Baire et espaces d'applications continues","volume":"301","author":"Calbrix","year":"1985","journal-title":"Comptes Rendus des S\u00e9ances de l'Acad\u00e9mie des Sciences, S\u00e9rie 1: Math\u00e9matique"},{"key":"S0022481200026591_ref004","first-page":"817","volume":"52","author":"Dougherty","year":"1987","journal-title":"Monotone but not positive subsets of the Cantor space"},{"key":"S0022481200026591_ref002","first-page":"655","article-title":"Filtres bor\u00e9liens sur l'ensemble des entiers et espaces des applications continues","volume":"33","author":"Calbrix","year":"1988","journal-title":"Revue Roumaine de Math\u00e9matique Pures et Appliqu\u00e9es"},{"key":"S0022481200026591_ref006","unstructured":"Dyck Stephen Douglas [1983], Some applications of positive formulas in descriptive set theory and logic, Ph.D. thesis, University of California, Berkeley, California."},{"key":"S0022481200026591_ref009","volume-title":"Le\u00e7ons sur les ensembles analytiques et leurs applications","author":"Luzin","year":"1930"},{"key":"S0022481200026591_ref010","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200026591_ref011","first-page":"A","volume-title":"Notices of the American Mathematical Society","volume":"19","author":"Wadge","year":"1972"},{"key":"S0022481200026591_ref014","volume-title":"Annals of Pure and Applied Logic","author":"Zafrany"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026591","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T17:52:12Z","timestamp":1558201932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026591\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["S0022481200026591"],"URL":"https:\/\/doi.org\/10.2307\/2274970","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}