{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T18:40:11Z","timestamp":1720723211144},"reference-count":17,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T00:00:00Z","timestamp":1540252800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"JSPS KAKENHI","award":["15K17587","15K04984"],"award-info":[{"award-number":["15K17587","15K04984"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a new combinatorial principle on singular cardinals. This principle allows us to take a kind of a diagonal intersection of more than \u03bb many measure one sets of certain normal ideals over<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700024-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700024:malq201700024-math-0001\"\/>. Under the principle, we give various characterizations of the saturation property of normal ideals over<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700024-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700024:malq201700024-math-0002\"\/>. We also consider Chang's type transfer properties under the principle, and, when \u03bb is J\u00f3nsson, we prove that every normal ideal over<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700024-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700024:malq201700024-math-0003\"\/>with<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700024-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700024:malq201700024-math-0004\"\/>measure one cannot have strong properties.<\/jats:p>","DOI":"10.1002\/malq.201700024","type":"journal-article","created":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T07:11:29Z","timestamp":1540365089000},"page":"395-408","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New combinatorial principle on singular cardinals and normal ideals"],"prefix":"10.1002","volume":"64","author":[{"given":"Toshimichi","family":"Usuba","sequence":"first","affiliation":[{"name":"Department of Pure and Applied Mathematics, Faculty of Science and Engineering Waseda University Okubo 3\u20104\u20101 Shinjuku Tokyo 169\u20108555 Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_15"},{"issue":"2","key":"e_1_2_8_3_1","first-page":"587","article-title":"Saturation properties of ideals in generic extensions. 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