{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T13:36:55Z","timestamp":1649165815184},"reference-count":9,"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":10054,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1986,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Suppose <jats:italic>\u03ba<\/jats:italic> is a supercompact cardinal. It is known that for every <jats:italic>\u03bb<\/jats:italic> \u2265 <jats:italic>\u03ba<\/jats:italic>, many normal ultrafilters on <jats:italic>P<jats:sub>\u03ba<\/jats:sub>(\u03bb)<\/jats:italic> have the partition property. It is also known that certain large cardinal assumptions imply the existence of normal ultrafilters without the partition property. In [1], we introduced the tree <jats:italic>T<\/jats:italic> of normal ultrafilters associated with <jats:italic>\u03ba<\/jats:italic>. We investigate the distribution throughout <jats:italic>T<\/jats:italic> of normal ultrafilters with and normal ultrafilters without the partition property.<\/jats:p>","DOI":"10.2307\/2274023","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:18:32Z","timestamp":1146953912000},"page":"701-708","source":"Crossref","is-referenced-by-count":0,"title":["Supercompact cardinals, trees of normal ultrafilters, and the partition property"],"prefix":"10.1017","volume":"51","author":[{"given":"Julius B.","family":"Barbanel","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200030863_ref002","first-page":"109","volume-title":"Finite and infinite sets ( P. Erd\u00f6s sixtieth birthday colloquium)","volume":"10","author":"Baumgartner","year":"1975"},{"key":"S0022481200030863_ref004","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":"S0022481200030863_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0281606"},{"key":"S0022481200030863_ref007","first-page":"225","volume":"41","author":"Menas","year":"1976","journal-title":"A combinatorial property of P\u03ba(\u03bb)"},{"key":"S0022481200030863_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1981-0601740-X"},{"key":"S0022481200030863_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S0022481200030863_ref001","first-page":"89","volume":"47","author":"Barbanel","year":"1982","journal-title":"Supercompact cardinals and trees of normal ultrafilters"},{"key":"S0022481200030863_ref003","unstructured":"Kunen K. , Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript (4 pages), 1971."},{"key":"S0022481200030863_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771565"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200030863","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T04:41:36Z","timestamp":1558500096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200030863\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1986,9]]}},"alternative-id":["S0022481200030863"],"URL":"https:\/\/doi.org\/10.2307\/2274023","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,9]]}}}