{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T05:01:16Z","timestamp":1649134876208},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7681,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Suppose <jats:italic>\u03ba<\/jats:italic> is a supercompact cardinal and <jats:italic>\u03bb<\/jats:italic> &gt; <jats:italic>\u03ba<\/jats:italic>. We study the relationship between the partition properly and the weak partition properly for normal ultrafilters on <jats:italic>P<jats:sub>\u03ba<\/jats:sub>\u03bb<\/jats:italic>. On the one hand, we show that the following statement is consistent, given an appropriate large cardinal assumption: The partition property and the weak partition properly are equivalent, there are many normal ultrafilters that satisfy these properties, and there are many normal ultrafilters that do not satisfy these properties. On the other hand, we consider the assumption that, for some <jats:italic>\u03bb<\/jats:italic> &gt; <jats:italic>\u03ba<\/jats:italic>, there exists a normal ultrafilter <jats:italic>U<\/jats:italic> on <jats:italic>P<jats:sub>\u03ba<\/jats:sub>\u03bb<\/jats:italic> such that <jats:italic>U<\/jats:italic> satisfies the weak partition property but does not satisfy the partition property. We show that this assumption is implied by the assertion that there exists a cardinal <jats:italic>\u03b3<\/jats:italic> &gt; <jats:italic>\u03ba<\/jats:italic> such that <jats:italic>\u03b3<\/jats:italic> is <jats:italic>\u03b3<\/jats:italic><jats:sup>+<\/jats:sup>-supercompact, and, assuming the GCH, it implies the assertion that there exists a cardinal <jats:italic>\u03b3<\/jats:italic> &gt; <jats:italic>\u03ba<\/jats:italic> such that <jats:italic>\u03b3<\/jats:italic> is a measurable cardinal with a normal ultrafilter concentrating on measurable cardinals.<\/jats:p>","DOI":"10.2307\/2275328","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:47:31Z","timestamp":1146941251000},"page":"119-127","source":"Crossref","is-referenced-by-count":0,"title":["On the relationship between the partition property and the weak partition property for normal ultrafilters on <i>P<sub>\u03ba<\/sub>\u03bb<\/i>"],"prefix":"10.1017","volume":"58","author":[{"given":"Julius B.","family":"Barbanel","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200021678_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1981-0601740-X"},{"key":"S0022481200021678_ref005","first-page":"475","volume":"48","author":"Kunen","year":"1983","journal-title":"On a combinatorial property of Menas related to the partition property for measures on supercompact cardinals"},{"key":"S0022481200021678_ref002","first-page":"109","volume-title":"Colloquia Mathematica Societatis Janos Bolyai","volume":"10","author":"Baumgartner","year":"1975"},{"key":"S0022481200021678_ref001","first-page":"701","volume":"51","author":"Barbanel","year":"1986","journal-title":"Supercompact cardinals, trees of normal ultrafilters, and the partition property"},{"key":"S0022481200021678_ref006","first-page":"225","volume":"41","author":"Menas","year":"1976","journal-title":"A combinatorial property of P\u03ba\u03bb"},{"key":"S0022481200021678_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(77)90088-3"},{"key":"S0022481200021678_ref004","unstructured":"Kunen K. , Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971."},{"key":"S0022481200021678_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200021678","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T15:14:40Z","timestamp":1558019680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200021678\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,3]]}},"alternative-id":["S0022481200021678"],"URL":"https:\/\/doi.org\/10.2307\/2275328","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}