{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T05:31:01Z","timestamp":1697693461009},"reference-count":8,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If <jats:italic>\u03ba<\/jats:italic> is an infinite cardinal, a complete Boolean algebra B is called <jats:italic>\u03ba<\/jats:italic>\u2010supported if for each sequence \u3008<jats:italic>b<jats:sub>\u03b2<\/jats:sub><\/jats:italic> : <jats:italic>\u03b2<\/jats:italic> &lt; <jats:italic>\u03ba<\/jats:italic>\u3009 of elements of B the equality <jats:styled-content>$ \\wedge$<\/jats:styled-content><jats:sub><jats:italic>\u03b1<\/jats:italic>&lt;<jats:italic>\u03ba<\/jats:italic><\/jats:sub> <jats:styled-content>$ \\vee$<\/jats:styled-content><jats:sub><jats:italic>\u03b2<\/jats:italic>&gt;<jats:italic>\u03b1<\/jats:italic><\/jats:sub> <jats:italic>b<jats:sub>\u03b2<\/jats:sub><\/jats:italic> = <jats:styled-content>$ \\vee$<\/jats:styled-content><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"equation\/tex2gif-inf-5.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ200410003:tex2gif-inf-5\" \/> <jats:styled-content>$ \\wedge$<\/jats:styled-content><jats:sub><jats:italic>\u03b2<\/jats:italic>\u2208<jats:italic>A<\/jats:italic><\/jats:sub> <jats:italic>b<\/jats:italic><jats:sub><jats:italic>\u03b2<\/jats:italic><\/jats:sub> holds. Combinatorial and forcing equivalents of this property are given and compared with the other forcing related properties of Boolean algebras (distributivity, caliber, etc.). The set of regular cardinals <jats:italic>\u03ba<\/jats:italic> for which B is not <jats:italic>\u03ba<\/jats:italic>\u2010supported is investigated. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200410003","type":"journal-article","created":{"date-parts":[[2004,10,4]],"date-time":"2004-10-04T16:01:01Z","timestamp":1096905661000},"page":"594-602","source":"Crossref","is-referenced-by-count":0,"title":["Unsupported Boolean algebras and forcing"],"prefix":"10.1002","volume":"50","author":[{"given":"Milo\u0161 S.","family":"Kurili\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,10]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"B.Balcar andP.Simon Disjoint refinement. In: Handbook of Boolean Algebra (J. D. Monk and R. Bonnet eds.) pp. 333\u2013386 (Elsevier Science Publishers B. V. Amsterdam 1989)."},{"key":"e_1_2_1_3_2","unstructured":"J. L.Bell Boolean\u2010Valued Models and Independence Proofs in Set Theory (Clarendon Press Oxford 1977)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90006-N"},{"key":"e_1_2_1_5_2","unstructured":"T.Jech Distributive laws. In: Handbook of Boolean Algebra (J. D. Monk and R. Bonnet eds.) pp. 317\u2013331 (Elsevier Science Publishers B. V. Amsterdam 1989)."},{"key":"e_1_2_1_6_2","unstructured":"T.Jech Set Theory (3rd edition) (Springer\u2010Verlag Berlin et al. 2003)."},{"key":"e_1_2_1_7_2","unstructured":"K.Kunen Set Theory: An Introduction to Independence Proofs (North\u2010Holland Publ. Comp. Amsterdam 1980)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(02)00067-2"},{"key":"e_1_2_1_9_2","first-page":"5","article-title":"Changing measurable into accessible cardinals","volume":"68","author":"Prikry K.","year":"1970","journal-title":"Diss. Math."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200410003","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200410003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T21:00:36Z","timestamp":1697662836000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200410003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":8,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1002\/malq.200410003"],"URL":"https:\/\/doi.org\/10.1002\/malq.200410003","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}