可计算可枚举集轨道的复杂性

IF 0.7 3区数学 Q1 LOGIC

Bulletin of Symbolic Logic Pub Date : 2008-03-01 DOI:10.2178/bsl/1208358844

Peter A. Cholak, R. Downey, L. Harrington

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引用次数: 3

摘要

摘要:本文的目的是宣布含有ε的c.e.集合存在一个单一轨道，从而使该轨道的隶属性问题完备。这个结果和证明有许多很好的推论:ε的Scott秩是+ 1;并非所有轨道都是基本可定义的;没有对ε的所有轨道的算术描述;对于所有有限α≥9，有一个合适的轨道(从证明)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Complexity of Orbits of Computably Enumerable Sets

Abstract The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is complete. This result and proof have a number of nice corollaries: the Scott rank of ε is + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly orbit (from the proof).

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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.