{"title":"A Hierarchy of computably Enumerable Degrees","authors":"R. Downey, Noam Greenberg","doi":"10.1017/BSL.2017.41","DOIUrl":null,"url":null,"abstract":"We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of ∆2 functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jocksuch and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"41 1","pages":"53-89"},"PeriodicalIF":0.7000,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Symbolic Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/BSL.2017.41","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 4
Abstract
We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of ∆2 functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jocksuch and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable
期刊介绍：
The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. It is designed to cover all areas within the purview of the ASL: mathematical logic and its applications, philosophical and non-classical logic and its applications, history and philosophy of logic, and philosophy and methodology of mathematics.
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