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Algebra i logika, 2022, Volume 61, Number 6, Pages 706–719
DOI: https://doi.org/10.33048/alglog.2022.61.603 (Mi al2738) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Families of permutations and ideals of Turing degrees

A. S. Morozova, V. G. Puzarenkoa, M. Kh. Faizrahmanovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Kazan (Volga Region) Federal University
Full-text PDF (195 kB) Citations (2)
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DOI: https://doi.org/10.33048/alglog.2022.61.603
Abstract: Families ${\mathcal P}_{\mathrm I}$ consisting of permutations of the natural numbers $\omega$ whose degrees belong to an ideal $\mathrm I$ of Turing degrees, as well as their jumps ${\mathcal P}'_{\mathrm I}$, are studied. For any countable Turing ideal $\mathrm I$, the degree spectra of families ${\mathcal P}_{\mathrm I}$ and their jumps ${\mathcal P}'_{\mathrm I}$ are described. For some ideals $\mathrm I$ generated by c.e. degrees, the spectra of families ${\mathcal P}_{\mathrm I}$ are defined.
Keywords: computable permutation, family of permutations, jump, Turing degree, ideal of Turing degrees, degree spectra.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00300 А
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0012
075-02-2022-882
Russian Science Foundation 22-21-20024
Supported by RFBR (project No. 20-01-00300 A) and by the Ministry of Education and Science of Russia (base project No. FWNF-2022-0012). Supported by Mathematical Center in Akademgorodok, Agreement No. 075-15-2022-281. The work was carried out as part of the developmental program for Scientific-Educational Mathematical Center (SEMC) in Volga Federal District (Agreement No. 075-02-2022-882) and supported by Russian Science Foundation (project No. 22-21-20024).
Received: 19.04.2022
Revised: 13.10.2023
English version:
Algebra and Logic, 2022, Volume 61, Issue 6, Pages 481–490
DOI: https://doi.org/10.1007/s10469-023-09714-1
Document Type: Article
UDC: 510.5
Language: Russian
Citation: A. S. Morozov, V. G. Puzarenko, M. Kh. Faizrahmanov, “Families of permutations and ideals of Turing degrees”, Algebra Logika, 61:6 (2022), 706–719; Algebra and Logic, 61:6 (2022), 481–490
Citation in format AMSBIB
\Bibitem{MorPuzFai22}
\by A.~S.~Morozov, V.~G.~Puzarenko, M.~Kh.~Faizrahmanov
\paper Families of permutations and ideals of Turing degrees
\jour Algebra Logika
\yr 2022
\vol 61
\issue 6
\pages 706--719
\mathnet{http://mi.mathnet.ru/al2738}
\transl
\jour Algebra and Logic
\yr 2022
\vol 61
\issue 6
\pages 481--490
\crossref{https://doi.org/10.1007/s10469-023-09714-1}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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