{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T21:07:28Z","timestamp":1775509648417,"version":"3.50.1"},"reference-count":40,"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":11607,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>\u03ba<jats:sub>B<\/jats:sub><\/jats:italic> be the least cardinal for which the Baire category theorem fails for the real line <jats:italic><jats:bold>R<\/jats:bold><\/jats:italic>. Thus <jats:italic>\u03ba<jats:sub>B<\/jats:sub><\/jats:italic> is the least <jats:italic>\u03ba<\/jats:italic> such that the real line can be covered by <jats:italic>\u03ba<\/jats:italic> many nowhere dense sets. It is shown that <jats:italic>\u03ba<jats:sub>B<\/jats:sub><\/jats:italic> cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2<jats:sup><jats:italic>\u03c9<jats:sub>1<\/jats:sub><\/jats:italic><\/jats:sup> be \u2135<jats:sub><jats:italic>\u03c9<\/jats:italic><\/jats:sub>. Similar questions are considered for the ideal of measure zero sets, other <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>, saturated ideals, and the ideal of zero-dimensional subsets of <jats:italic><jats:bold>R<\/jats:bold><jats:sup>\u03c9<jats:sub>1<\/jats:sub><\/jats:sup><\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273142","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:59:42Z","timestamp":1146938382000},"page":"275-288","source":"Crossref","is-referenced-by-count":17,"title":["The Baire category theorem and cardinals of countable cofinality"],"prefix":"10.1017","volume":"47","author":[{"given":"Arnold W.","family":"Miller","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044248_ref030","first-page":"179","volume":"42","author":"Pincus","year":"1977","journal-title":"Definability of measures and ultrafilters"},{"key":"S0022481200044248_ref028","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90009-4"},{"key":"S0022481200044248_ref025","volume-title":"Set theory","author":"Kunen","year":"1980"},{"key":"S0022481200044248_ref022","volume-title":"Cardinal functions in topology","author":"Juhasz","year":"1971"},{"key":"S0022481200044248_ref020","doi-asserted-by":"publisher","DOI":"10.4064\/fm-19-1-8-9"},{"key":"S0022481200044248_ref031","doi-asserted-by":"publisher","DOI":"10.4064\/fm-93-1-57-69"},{"key":"S0022481200044248_ref019","first-page":"916","article-title":"Uber unendlichdimensionale Punktmengen","volume":"31","author":"Hurewicz","year":"1928","journal-title":"Koninklijke Nederlandse Akademie van Wetenschappen. 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