The singleton degrees of the Σ20 sets are not dense

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-05-27 DOI:10.1016/j.apal.2025.103616

Thomas F. Kent , Keng Meng Ng , Andrea Sorbi

引用次数: 0

Abstract

Answering an open question raised by Cooper, we show that there exist

Δ_{2}^{0}

sets D and E such that the singleton degree of E is a minimal cover of the singleton degree of D. This shows that the

Σ_{2}^{0}

singleton degrees, and the

Δ_{2}^{0}

singleton degrees, are not dense (and consequently the

Π_{2}^{0}

Q-degrees, and the

Δ_{2}^{0}

Q-degrees, are not dense). Moreover, D and E can be built to lie in the same enumeration degree.

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Σ20集合的单态度是不密集的

回答Cooper提出的一个开放性问题，我们证明存在Δ20集合D和E，使得E的单态度是D的单态度的最小覆盖。这表明Σ20单态度和Δ20单态度不是密集的（因此Π20 q度和Δ20 q度不是密集的）。而且，D和E可以构建在同一枚举度。

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.