{"title":"可构造度的广度和可定义的西尔皮斯基覆盖层","authors":"Alessandro Andretta, Lorenzo Notaro","doi":"arxiv-2408.10182","DOIUrl":null,"url":null,"abstract":"Generalizing a result of T\\\"ornquist and Weiss, we study the connection\nbetween the existence of $\\varSigma_2^1$ Sierpi\\'{n}ski's coverings of\n$\\mathbb{R}^n$, and a cardinal invariant of the upper semi-lattice of\nconstructibility degrees known as breadth.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The breadth of constructibility degrees and definable Sierpiński's coverings\",\"authors\":\"Alessandro Andretta, Lorenzo Notaro\",\"doi\":\"arxiv-2408.10182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Generalizing a result of T\\\\\\\"ornquist and Weiss, we study the connection\\nbetween the existence of $\\\\varSigma_2^1$ Sierpi\\\\'{n}ski's coverings of\\n$\\\\mathbb{R}^n$, and a cardinal invariant of the upper semi-lattice of\\nconstructibility degrees known as breadth.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.10182\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.10182","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The breadth of constructibility degrees and definable Sierpiński's coverings
Generalizing a result of T\"ornquist and Weiss, we study the connection
between the existence of $\varSigma_2^1$ Sierpi\'{n}ski's coverings of
$\mathbb{R}^n$, and a cardinal invariant of the upper semi-lattice of
constructibility degrees known as breadth.
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