{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T08:25:55Z","timestamp":1717230355272},"reference-count":11,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2015,11,19]],"date-time":"2015-11-19T00:00:00Z","timestamp":1447891200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Japan-Austria Research Cooperative Program","award":["15K17587"],"award-info":[{"award-number":["15K17587"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p>We study the subtlety of a cardinal \u03ba and of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0001\" \/>. We show that, under a certain large cardinal assumption, it is consistent that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0002\" \/> is subtle for some <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0003\" \/> but \u03ba is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0004\" \/> can be characterized by a certain partition relation on <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0005\" \/>. We also study the property of faintness of \u03ba, and the subtlety of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400040-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400040:malq201400040-math-0006\" \/> with the strong inclusion.<\/jats:p>","DOI":"10.1002\/malq.201400040","type":"journal-article","created":{"date-parts":[[2015,11,19]],"date-time":"2015-11-19T15:15:19Z","timestamp":1447946119000},"page":"59-71","source":"Crossref","is-referenced-by-count":1,"title":["Subtlety and partition relations"],"prefix":"10.1002","volume":"62","author":[{"given":"Toshimichi","family":"Usuba","sequence":"first","affiliation":[{"name":"Organization of Advanced Science and Technology Kobe University Rokko\u2010dai 1\u20101 Nada Kobe 657\u20108501 Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2015,11,19]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-004-0272-9"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-012-0283-x"},{"key":"e_1_2_9_4_1","volume-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai Vol. 10","author":"Baumgartner J. 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B.","year":"2004"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19880340211"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90009-1"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200051926"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201400040","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T20:24:20Z","timestamp":1696364660000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201400040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,19]]},"references-count":11,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["10.1002\/malq.201400040"],"URL":"https:\/\/doi.org\/10.1002\/malq.201400040","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,19]]}}}