{"title":"κ-Madness and definability","authors":"Haim Horowitz, Saharon Shelah","doi":"10.1002/malq.202100074","DOIUrl":null,"url":null,"abstract":"<p>Assuming the existence of a supercompact cardinal, we construct a model where, for some uncountable regular cardinal κ, there are no <math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>1</mn>\n </msubsup>\n <mrow>\n <mo>(</mo>\n <mi>κ</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\Sigma ^1_1(\\kappa )$</annotation>\n </semantics></math> κ-mad families.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202100074","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
Assuming the existence of a supercompact cardinal, we construct a model where, for some uncountable regular cardinal κ, there are no κ-mad families.
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