可计算可枚举度的层次结构

IF 0.7 3区数学 Q1 LOGIC

Bulletin of Symbolic Logic Pub Date : 2018-03-01 DOI:10.1017/BSL.2017.41

R. Downey, Noam Greenberg

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引用次数: 4

摘要

我们引入了一种新的可计算枚举度的层次结构。这个层次是基于测量∆2函数近似复杂度的可计算有序符号。在可计算理论中，层次结构统一和分类了许多不同结构的组合。它按照高度数(Martin)和数组不可计算度数(Downey, Jocksuch和Stob)的顺序进行操作。层次结构还给出了一些自然的可定义性结果，包括一个可定义的

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A Hierarchy of computably Enumerable Degrees

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

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来源期刊

Bulletin of Symbolic Logic 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

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.