{"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}
引用次数: 0
Abstract
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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