{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:50:51Z","timestamp":1759146651189},"reference-count":28,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>Our main results are: (A) It is consistent relative to a large cardinal that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0001\" \/> holds but <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0002\" \/> fails. (B) If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0003\" \/> holds and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0004\" \/> are two infinite cardinals such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0005\" \/> and \u03bb carries a good scale, then <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0006\" \/> holds. (C) If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0007\" \/> are two cardinals such that \u03ba is \u03bb\u2010Shelah and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200008-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201200008:malq201200008-math-0008\" \/>, then there is no good scale for \u03bb.<\/jats:p>","DOI":"10.1002\/malq.201200008","type":"journal-article","created":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T07:59:32Z","timestamp":1406879972000},"page":"246-265","source":"Crossref","is-referenced-by-count":9,"title":["Two\u2010cardinal diamond star"],"prefix":"10.1002","volume":"60","author":[{"given":"Pierre","family":"Matet","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Caen and CNRS Laboratoire de Math\u00e9matiques Nicolas Oresme BP 5186 14032 Caen cedex France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2014,8]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050097"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_15"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1041044-9"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021906130100003X"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.04.002"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764635"},{"key":"e_1_2_10_8_1","volume-title":"Birkh\u00e4user Advanced Texts: Basler Lehrb\u00fccher","author":"Holz M.","year":"1999"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01903842"},{"key":"e_1_2_10_10_1","unstructured":"K.Kojman Splitting families of sets in preprint."},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1122038913"},{"key":"e_1_2_10_12_1","volume-title":"Studies in Logic and the Foundations of Mathematics","author":"Kunen K.","year":"1980"},{"key":"e_1_2_10_13_1","unstructured":"J.P.Levinski On the principle unpublished."},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02937302"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1164060456"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm205-1-3"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.022"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1305810755"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200810064"},{"key":"e_1_2_10_20_1","unstructured":"P.Matet Ideals onassociated with games of uncountable length Arch. 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