{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T07:40:33Z","timestamp":1698392433548},"reference-count":6,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3969,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For any Boolean Algebra <jats:italic>A<\/jats:italic>, let c<jats:sub>mm<\/jats:sub>(<jats:italic>A<\/jats:italic>) be the smallest size of an infinite partition of unity in <jats:italic>A.<\/jats:italic> The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which c<jats:sub>mm<\/jats:sub> exceeds any preassigned number, a rigid interval algebra with that property, and the construction of an interval algebra in which every well\u2010ordered chain has size less than c<jats:sub>mm<\/jats:sub>.<\/jats:p><jats:p>Mathematics Subject Classification: 06E05, 03E05.<\/jats:p>","DOI":"10.1002\/malq.19960420142","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T15:26:51Z","timestamp":1180538811000},"page":"537-550","source":"Crossref","is-referenced-by-count":2,"title":["Minimum\u2010sized Infinite Partitions of Boolean Algebras"],"prefix":"10.1002","volume":"42","author":[{"given":"J.","family":"Donald Monk","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Theory of Ultrafilters","author":"Comfort W. W.","year":"1982"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-86580-9.50006-9"},{"key":"e_1_2_1_4_2","volume-title":"General Theory of Boolean algebras. Handbook of Boolean Algebras","author":"Koppelberg S.","year":"1989"},{"key":"e_1_2_1_5_2","volume-title":"Cardinal Invariants on Boolean Algebras","author":"Monk J. D.","year":"1995"},{"key":"e_1_2_1_6_2","volume-title":"Linear Orderings","author":"Rosenstein J.","year":"1982"},{"key":"e_1_2_1_7_2","first-page":"267","article-title":"Very strongly rigid Boolean algebras","volume":"27","author":"Todor\u010devi\u010d S.","year":"1980","journal-title":"Publ. Inst. Math. (Beograd)"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19960420142","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19960420142","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T22:13:14Z","timestamp":1698358394000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19960420142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["10.1002\/malq.19960420142"],"URL":"https:\/\/doi.org\/10.1002\/malq.19960420142","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,1]]}}}