{"title":"一个友好的迭代，强制$\\mathcal E$的四个基本特征可以成对不同","authors":"Miguel Alvarado Cardona","doi":"10.4064/cm8917-2-2023","DOIUrl":null,"url":null,"abstract":"Let $\\mathcal{E}$ be the $\\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\\mathcal{E}$, their associated cardinal characteristics (i.e.\\ additivity, covering, uniformity and cofinality) are pairwise different.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A friendly iteration forcing that the four cardinal characteristics of $\\\\mathcal E$ can be pairwise different\",\"authors\":\"Miguel Alvarado Cardona\",\"doi\":\"10.4064/cm8917-2-2023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\mathcal{E}$ be the $\\\\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\\\\mathcal{E}$, their associated cardinal characteristics (i.e.\\\\ additivity, covering, uniformity and cofinality) are pairwise different.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/cm8917-2-2023\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/cm8917-2-2023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A friendly iteration forcing that the four cardinal characteristics of $\mathcal E$ can be pairwise different
Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\ additivity, covering, uniformity and cofinality) are pairwise different.
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