{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T11:47:51Z","timestamp":1774439271656,"version":"3.50.1"},"reference-count":25,"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":2476,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.<\/jats:p>","DOI":"10.2178\/jsl\/1185803621","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:24:48Z","timestamp":1198081488000},"page":"501-512","source":"Crossref","is-referenced-by-count":44,"title":["Ideal convergence of bounded sequences"],"prefix":"10.1017","volume":"72","author":[{"given":"Rafa\u0142","family":"Filip\u00f3w","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikodem","family":"Mro\u017cek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ireneusz","family":"Rec\u0142aw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Szuca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005338_ref022","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-56-02337-7"},{"key":"S0022481200005338_ref020","first-page":"1928","volume":"66","author":"Monk","year":"2001","journal-title":"Continuum cardinals generalized to Boolean algebras"},{"key":"S0022481200005338_ref023","first-page":"279","article-title":"On some properties of J-convergence","volume":"28","author":"\u0160al\u00e1t","year":"2004","journal-title":"Tatra Mountains Mathematical Publications"},{"key":"S0022481200005338_ref005","first-page":"23","article-title":"The sequentiality is equivalent to the F-Fr\u00e9chet-Urysohn property","volume":"31","author":"Boldjiev","year":"1990","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481200005338_ref016","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-01-06116-0"},{"key":"S0022481200005338_ref021","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6778"},{"key":"S0022481200005338_ref025","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00051-7"},{"key":"S0022481200005338_ref012","first-page":"411","article-title":"On certain Boolean algebras P (\u03c9)\/I","volume":"285","author":"Just","year":"1984","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200005338_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm183-1-4"},{"key":"S0022481200005338_ref002","doi-asserted-by":"publisher","DOI":"10.14321\/realanalexch.30.1.0267"},{"key":"S0022481200005338_ref003","first-page":"95","article-title":"Structural properties of ideals","volume":"197","author":"Baumgartner","year":"1982","journal-title":"Polska Akademia Nauk. 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