Permutation Groups and Ideals of Turing Degrees

Permutation Groups and Ideals of Turing Degrees Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2025, Volume: 63, Number: 2, Pages: 141-152 Pages count : 12 DOI: 10.1007/s10469-025-09777-2

Tags

computable permutation, permutation group, Turing degree, Turing ideal, degree of permutation group, degree spectrum.

Authors

Morozov A.S. ^1,2 , Puzarenko V.G. ^1,2 , Faizrakhmanov M.Kh. ^3,4

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Novosibirsk State University, Novosibirsk, Russia
3	Kazan (Volga Region) Federal University, Kazan, Russia
4	Science Education Mathematical Center of Volga Federal District, Kazan, Russia

Funding (3)

1	Sobolev Institute of Mathematics	FWNF-2022-0012
2	Mathematical Center in Akademgorodok	075-15-2022-282
3	Kazan Federal University	075-02-2022-882

We study degrees and degree spectra of groups GI defined on a set of permutations of the natural numbers ω whose degrees belong to a Turing ideal I. A necessary condition and a sufficient condition are stated which specify whether an arbitrary Turing degree belongs to the degree spectrum of a group GI. Nonprincipal ideals I for which the group GI has or does not have a degree are exemplified.

Morozov A.S. , Puzarenko V.G. , Faizrakhmanov M.K.
Permutation Groups and Ideals of Turing Degrees
Algebra and Logic. 2025. V.63. N2. P.141-152. DOI: 10.1007/s10469-025-09777-2 WOS Scopus РИНЦ OpenAlex

Морозов А.С. , Пузаренко В.Г. , Файзрахманов М.Х.
Группы перестановок и идеалы тьюринговых степеней
Алгебра и логика. 2024. Т.63. №2. С.209-224. DOI: 10.33048/alglog.2024.63.205 РИНЦ

Submitted:	Sep 14, 2022
Accepted:	Dec 6, 2024
Published print:	Jan 22, 2025
Published online:	Jan 22, 2025

Web of science:	WOS:001401863000001
Scopus:	2-s2.0-85217432183
Elibrary:	81144944
OpenAlex:	W4406724708

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