{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T15:37:44Z","timestamp":1726069064993},"reference-count":21,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T00:00:00Z","timestamp":1326931200000},"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":[[2012,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a regular uncountable cardinal \u03ba and a cardinal \u03bb &gt; \u03ba of cofinality \u03c9, we show that the restriction of the non\u2010stationary ideal on<jats:italic>P<\/jats:italic><jats:sub>\u03ba<\/jats:sub>(\u03bb) to the set of all<jats:italic>a<\/jats:italic>with<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{cf}(\\sup (a\\cap \\kappa)) = \\omega$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>is not \u03bb<jats:sup>++<\/jats:sup>\u2010saturated (and even not<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$2^{{(\\lambda ^{&lt;\\kappa }})}$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-2.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>\u2010saturated in case 2<jats:sup>\u03bb<\/jats:sup>= \u03bb<jats:sup>+<\/jats:sup>). We actually prove the stronger result that there is<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$Q\\subseteq \\mathrm{NG}_{\\kappa ,\\lambda }^+$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-3.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>with |<jats:italic>Q<\/jats:italic>| = \u03bb<jats:sup>++<\/jats:sup>such that<jats:italic>A<\/jats:italic>\u2229<jats:italic>B<\/jats:italic>is a non\u2010cofinal subset of<jats:italic>P<\/jats:italic><jats:sub>\u03ba<\/jats:sub>(\u03bb) for any two distinct members<jats:italic>A<\/jats:italic>,<jats:italic>B<\/jats:italic>of<jats:italic>Q<\/jats:italic>, where NG<jats:sub>\u03ba, \u03bb<\/jats:sub>denotes the game ideal on<jats:italic>P<\/jats:italic><jats:sub>\u03ba<\/jats:sub>(\u03bb). We also remark that for \u03ba &gt; \u03c9<jats:sub>1<\/jats:sub>, adding \u03bb<jats:sup>+3<\/jats:sup>Cohen subsets of \u03c9<jats:sub>1<\/jats:sub>to<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathbf {L}$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-4.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>makes NG<jats:sub>\u03ba, \u03bb<\/jats:sub>\u03bb<jats:sup>+3<\/jats:sup>\u2010saturated.<\/jats:p>","DOI":"10.1002\/malq.201020055","type":"journal-article","created":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T10:00:52Z","timestamp":1326967252000},"page":"38-45","source":"Crossref","is-referenced-by-count":3,"title":["Non\u2010saturation of the non\u2010stationary ideal on<i>P<\/i><sub>\u03ba<\/sub>(\u03bb) with \u03bb of countable cofinality"],"prefix":"10.1002","volume":"58","author":[{"given":"Pierre","family":"Matet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,1,19]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/04830511"},{"key":"e_1_2_7_3_1","first-page":"333","volume-title":"Handbook of Boolean Algebras","author":"Balcar B.","year":"1989"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90018-8"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_16"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401842"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03702-7"},{"key":"e_1_2_7_8_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0346-0330-0","volume-title":"Introduction to Cardinal Arithmetic, Birkh\u00e4user Advanced Texts, Basler Lehrb\u00fccher","author":"Holz M.","year":"1999"},{"key":"e_1_2_7_9_1","volume-title":"Set Theory, Springer Monographs in Mathematics third millenium ed.","author":"Jech T.","year":"2002"},{"key":"e_1_2_7_10_1","volume-title":"Set Theory, An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics Vol. 102","author":"Kunen K.","year":"1980"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/2001455"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2008-057-5"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.022"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200810064"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02762383"},{"key":"e_1_2_7_16_1","unstructured":"P.Matet C.P\u00e9an andS.Shelah Cofinality of normal ideals onP\u03ba(\u03bb) I preprint."},{"key":"e_1_2_7_17_1","unstructured":"P.MatetandS.Shelah The nonstationary ideal onP\u03ba(\u03bb) for \u03bb singular preprint."},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03202-1"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90075-3"},{"key":"e_1_2_7_20_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal Arithmetic, Oxford Logic Guides Vol. 29","author":"Shelah S.","year":"1994"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm198-2-1"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm205-3-4"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020055","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020055","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201020055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T00:50:15Z","timestamp":1713401415000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201020055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,19]]},"references-count":21,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["10.1002\/malq.201020055"],"URL":"https:\/\/doi.org\/10.1002\/malq.201020055","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,19]]}}}