{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T05:40:17Z","timestamp":1696052417243},"reference-count":12,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"South African Foundation of Research and Development"},{"name":"University of Cape Town Research Committee"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For an infinite cardinal <jats:italic>K<\/jats:italic> a stronger version of <jats:italic>K<\/jats:italic>\u2010distributivity for Boolean algebras, called k\u2010partition completeness, is defined and investigated (e. g. every <jats:italic>K<\/jats:italic>\u2010Suslin algebra is a <jats:italic>K<\/jats:italic>\u2010partition complete Boolean algebra). It is shown that every <jats:italic>k<\/jats:italic>\u2010partition complete Boolean algebra is <jats:italic>K<\/jats:italic>\u2010weakly representable, and for strongly inaccessible <jats:italic>K<\/jats:italic> these concepts coincide. For regular <jats:italic>K<\/jats:italic> \u2265 <jats:italic>u<\/jats:italic>, it is proved that an atomless <jats:italic>K<\/jats:italic>\u2010partition complete Boolean algebra is an updirected union of basic <jats:italic>K<\/jats:italic>\u2010tree algebras. Using K\u2010partition completeness, the concept of \u03b3\u2010almost compactness is introduced for \u03b3 \u2265 <jats:italic>K<\/jats:italic>. For strongly inaccessible <jats:italic>K<\/jats:italic> we show that <jats:italic>K<\/jats:italic> is K\u2010almost compact iff <jats:italic>K<\/jats:italic> is weakly compact, and if <jats:italic>K<\/jats:italic> is 2<jats:sup>K<\/jats:sup>\u2010almost compact, then <jats:italic>K<\/jats:italic> is measurable. Further <jats:italic>K<\/jats:italic> is strongly compact iff it is \u03b3\u2010almost compact for all \u03b3 \u2265 <jats:italic>K.<\/jats:italic><\/jats:p>","DOI":"10.1002\/malq.19990450208","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T16:30:55Z","timestamp":1290011455000},"page":"241-255","source":"Crossref","is-referenced-by-count":0,"title":["Partition Complete Boolean Algebras and Almost Compact Cardinals"],"prefix":"10.1002","volume":"45","author":[{"given":"Peter","family":"Jipsen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henry","family":"Rose","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Model Theory","author":"Chang C. C","year":"1977"},{"key":"e_1_2_1_3_2","volume-title":"Set Theory","author":"Drake F. R.","year":"1974"},{"key":"e_1_2_1_4_2","first-page":"50","volume-title":"Essays on the Foundation of Mathematics","author":"Erd\u00d6S P.","year":"1961"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-51-3-195-228"},{"key":"e_1_2_1_6_2","volume-title":"Set Theory","author":"Jech T. J.","year":"1978"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-53-3-225-308"},{"key":"e_1_2_1_8_2","volume-title":"Handbook of Boolean Algebras","author":"Koppelberg S.","year":"1989"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02308-2"},{"key":"e_1_2_1_10_2","first-page":"313","article-title":"The model correspondences","volume":"23","author":"Mal'CEV A. I.","year":"1959","journal-title":"Izvestia AN SSSR, Ser. Math."},{"key":"e_1_2_1_10_3","first-page":"66","volume-title":"Metamathematics of Algebraic Systems","year":"1971"},{"key":"e_1_2_1_11_2","volume-title":"Handbook of Boolean Algebras","author":"Monk J. D.","year":"1989"},{"key":"e_1_2_1_12_2","unstructured":"Ouwehand P. andH.Rose Filtral powers of structures. J. Symbolic Logic (to appear)"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450208","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450208","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19990450208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T19:18:06Z","timestamp":1696015086000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19990450208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1002\/malq.19990450208"],"URL":"https:\/\/doi.org\/10.1002\/malq.19990450208","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}