Strong minimal pairs in the enumeration degrees

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-05-28 DOI:10.1016/j.apal.2024.103464

Josiah Jacobsen-Grocott

引用次数: 0

Abstract

We prove that there are strong minimal pairs in the enumeration degrees and that the degrees of the left and right sides of strong minimal pairs include $Σ_{2}^{0}$ degrees, although it is unknown if there is a strong minimal pair in the $Σ_{2}^{0}$ enumeration degrees. We define a stronger type of minimal pair we call a strong super minimal pair, and show that there are none of these in the enumeration degrees, answering a question of Lempp et al. [6]. We leave open the question of the existence of a super minimal pair in the enumeration degrees.

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枚举度中的强最小对

我们证明了在枚举度中存在强极小对，并且强极小对的左侧和右侧的度包括 Σ20 度，尽管在 Σ20 枚举度中是否存在强极小对还是未知数。我们定义了一种更强的极小对，称为强超极小对，并证明在枚举度中不存在强超极小对，从而回答了 Lempp 等人提出的问题[6]。我们对枚举度中是否存在超极小对这个问题保持开放态度。

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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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.