On -tardy sets

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• 作者：Peter A. Cholak^a ; ^{Peter.Cholak.1@nd.edu} ; ; Peter M. Gerdes^a ; ^{gerdes@invariant.org} ; ; Karen Lange^b ; ^{klange2@wellesley.edu} ;
• 关键词：03D25 ; 03D30
• 刊名：Annals of Pure and Applied Logic
• 出版年：2012
• 期刊代码：4_01680072
• 类别：cp
• 出版时间：September, 2012
• 卷：163
• 期：9
• 页码：1252-1270
• 文件大小：358 K

摘要

Harrington and Soare introduced the notion of an -tardy set. They showed that there is a nonempty property such that if then is -tardy. Since they also showed no -tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of -tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about -tardy sets. We show there is a -tardy set that is not computed by any -tardy set . We also show that there are nonempty properties such that if then is properly -tardy.