可计算可枚举集轨道的复杂性

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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