{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T08:52:15Z","timestamp":1698655935985},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3479,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>Assume that all algebras are atomless. (1) Spind(<jats:italic>A<\/jats:italic> \u00d7 <jats:italic>B<\/jats:italic>) = Spind(<jats:italic>A<\/jats:italic>) \u222a Spind(<jats:italic>B<\/jats:italic>). (2) <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120000757X_inline3\" \/> Spind(<jats:italic>A<jats:sub>i<\/jats:sub><\/jats:italic>). Now suppose that <jats:italic>\u03ba<\/jats:italic> and <jats:italic>\u03bb<\/jats:italic> are infinite cardinals, with \u03ba uncountable and regular and with <jats:italic>\u03ba<\/jats:italic> &lt; <jats:italic>\u03bb<\/jats:italic>. (3) There is an atomless Boolean algebra <jats:italic>A<\/jats:italic> such that u(<jats:italic>A<\/jats:italic>) = <jats:italic>\u03ba<\/jats:italic> and <jats:italic>i<\/jats:italic>(<jats:italic>A<\/jats:italic>) = <jats:italic>\u03bb<\/jats:italic>. (4) If <jats:italic>\u03bb<\/jats:italic> is also regular, then there is an atomless Boolean algebra <jats:italic>A<\/jats:italic> such that t(<jats:italic>A<\/jats:italic>) = <jats:italic>s<\/jats:italic>(<jats:italic>A<\/jats:italic>) = <jats:italic>\u03ba<\/jats:italic> and <jats:italic>\u03b1<\/jats:italic> (<jats:italic>A<\/jats:italic>) = <jats:italic>\u03bb<\/jats:italic>. All results are in ZFC, and answer some problems posed in Monk [01] and Monk [\u221e].<\/jats:p>","DOI":"10.2178\/jsl\/1096901761","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:41:13Z","timestamp":1109799673000},"page":"674-682","source":"Crossref","is-referenced-by-count":3,"title":["On some small cardinals for Boolean algebras"],"prefix":"10.1017","volume":"69","author":[{"given":"Ralph","family":"Mckenzie","sequence":"first","affiliation":[]},{"given":"J. Donald","family":"Monk","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000757X_ref005","volume-title":"Proceedings of the 2001 Tarski Symposium","author":"Monk"},{"key":"S002248120000757X_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90082-0"},{"key":"S002248120000757X_ref004","first-page":"1928","volume":"66","author":"Monk","year":"2001","journal-title":"Continuum cardinals generalized to Boolean algebras"},{"key":"S002248120000757X_ref001","first-page":"333","volume-title":"Handbook of Boolean algebras","volume":"2","author":"Balcar","year":"1989"},{"key":"S002248120000757X_ref003","volume-title":"Handbook of Boolean algebras","volume":"1","author":"Koppelberg","year":"1989"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000757X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:26:55Z","timestamp":1557174415000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000757X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,9]]}},"alternative-id":["S002248120000757X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1096901761","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,9]]}}}