{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T22:36:58Z","timestamp":1781563018167,"version":"3.54.5"},"reference-count":15,"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":3663,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A family <jats:italic>A<\/jats:italic> \u2286 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200008057_inline1\"\/>(<jats:italic>\u03c9<\/jats:italic>) is called countably splitting if for every countable <jats:italic>F<\/jats:italic> \u2286 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup>, some element of <jats:italic>A<\/jats:italic> splits every member of <jats:italic>F<\/jats:italic>. We define a notion of a splitting tree, by means of which we prove that every analytic countably splitting family contains a closed countably splitting family. An application of this notion solves a problem of Blass. On the other hand we show that there exists an <jats:italic>F<jats:sub>\u03c3<\/jats:sub><\/jats:italic> splitting family that does not contain a closed splitting family.<\/jats:p>","DOI":"10.2178\/jsl\/1080938830","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:26:59Z","timestamp":1109798819000},"page":"101-117","source":"Crossref","is-referenced-by-count":8,"title":["Analytic countably splitting families"],"prefix":"10.1017","volume":"69","author":[{"given":"Otmar","family":"Spinas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200008057_ref001","first-page":"31","volume-title":"Set theory (Annual Boise extravaganza in set theory conference, 1992\u201394)","volume":"192","author":"Blass","year":"1996"},{"key":"S0022481200008057_ref010","first-page":"1179","volume":"62","author":"Mildenberger","year":"1997","journal-title":"Non-constructive Galois-Tukey connections"},{"key":"S0022481200008057_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00027-Z"},{"key":"S0022481200008057_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90025-6"},{"key":"S0022481200008057_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1977-0450070-1"},{"key":"S0022481200008057_ref011","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1002\/1521-3870(200211)48:4<517::AID-MALQ517>3.0.CO;2-#","article-title":"No Borel connections for the unsplitting relations","volume":"48","author":"Martin","year":"2002","journal-title":"Mathematical Logic Quarterly"},{"key":"S0022481200008057_ref012","first-page":"85","article-title":"Approximation des sous-ensembles analytiques par l'int\u00e9rieur","volume":"281","author":"Raymond","year":"1975","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences Paris, S\u00e9rie A"},{"key":"S0022481200008057_ref014","first-page":"619","volume-title":"Set theory of the reals","volume":"6","author":"Vojt\u00e1\u0161","year":"1993"},{"key":"S0022481200008057_ref007","volume-title":"Set theory, An introduction to independence proofs","author":"Kunen","year":"1983"},{"key":"S0022481200008057_ref015","unstructured":"Yiparaki O. , On some tree partitions, Ph.D. thesis , University of Michigan, 1994."},{"key":"S0022481200008057_ref002","volume-title":"Handbook of Set Theory","author":"Blass"},{"key":"S0022481200008057_ref008","volume-title":"Topology","volume":"1","author":"Kuratowski","year":"1980"},{"key":"S0022481200008057_ref004","first-page":"85","article-title":"Infinite games of perfect information","volume":"52","author":"Davis","year":"1964","journal-title":"Annals of Mathematics Studies"},{"key":"S0022481200008057_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1971035"},{"key":"S0022481200008057_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200008057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:29:08Z","timestamp":1557178148000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200008057\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["S0022481200008057"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1080938830","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}