{"title":"CONSTRUCTING MAXIMAL COFINITARY GROUPS","authors":"David Schrittesser","doi":"10.1017/nmj.2022.46","DOIUrl":null,"url":null,"abstract":"Abstract Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in \n$\\mathsf {ZF}$\n , i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2022.46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in
$\mathsf {ZF}$
, i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.
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