Families of Permutations and Ideals of Turing Degrees

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2023-12-04 DOI:10.1007/s10469-023-09714-1

A. S. Morozov, V. G. Puzarenko, M. Kh. Faizrachmanov

引用次数: 0

Abstract

Families 𝒫_I consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps \({\mathcal{P}}_{\mathrm{I}}{\prime}\), are studied. For any countable Turing ideal I, the degree spectra of families 𝒫_I and their jumps \({\mathcal{P}}_{\mathrm{I}}{\prime}\) are described. For some ideals I generated by c.e. degrees, the spectra of families 𝒫_I are defined.

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排列族与图灵度理想

研究了由度属于图灵度的理想I的自然数ω的排列组成的族𝒫I及其跳跃\({\mathcal{P}}_{\mathrm{I}}{\prime}\)。对于任意可数图灵理想I，描述了族的度谱𝒫I及其跳变\({\mathcal{P}}_{\mathrm{I}}{\prime}\)。对于一些由c.e.度产生的理想I，定义了族𝒫I的光谱。

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

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.