Standard

Families of Permutations and Ideals of Turing Degrees. / Morozov, A. S.; Puzarenko, V. G.; Faizrachmanov, M. Kh.

In: Algebra and Logic, Vol. 61, No. 6, 01.2023, p. 481-490.

Research output: Contribution to journal › Article › peer-review

Harvard

Morozov, AS, Puzarenko, VG & Faizrachmanov, MK 2023, 'Families of Permutations and Ideals of Turing Degrees', Algebra and Logic, vol. 61, no. 6, pp. 481-490. https://doi.org/10.1007/s10469-023-09714-1

APA

Morozov, A. S., Puzarenko, V. G., & Faizrachmanov, M. K. (2023). Families of Permutations and Ideals of Turing Degrees. Algebra and Logic, 61(6), 481-490. https://doi.org/10.1007/s10469-023-09714-1

Vancouver

Morozov AS, Puzarenko VG, Faizrachmanov MK. Families of Permutations and Ideals of Turing Degrees. Algebra and Logic. 2023 Jan;61(6):481-490. doi: 10.1007/s10469-023-09714-1

Author

Morozov, A. S. ; Puzarenko, V. G. ; Faizrachmanov, M. Kh. / Families of Permutations and Ideals of Turing Degrees. In: Algebra and Logic. 2023 ; Vol. 61, No. 6. pp. 481-490.

BibTeX

@article{0558ad7372244b85bea3cad094d9624c,
title = "Families of Permutations and Ideals of Turing Degrees",
abstract = "Families PI consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps PI′ , are studied. For any countable Turing ideal I, the degree spectra of families PI and their jumps PI′ are described. For some ideals I generated by c.e. degrees, the spectra of families PI are defined.",
keywords = "Turing degree, computable permutation, degree spectra, family of permutations, ideal of Turing degrees, jump",
author = "Morozov, {A. S.} and Puzarenko, {V. G.} and Faizrachmanov, {M. Kh}",
note = "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). 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).",
year = "2023",
month = jan,
doi = "10.1007/s10469-023-09714-1",
language = "English",
volume = "61",
pages = "481--490",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Families of Permutations and Ideals of Turing Degrees

AU - Morozov, A. S.

AU - Puzarenko, V. G.

AU - Faizrachmanov, M. Kh

N1 - 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). 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).

PY - 2023/1

Y1 - 2023/1

N2 - Families PI consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps PI′ , are studied. For any countable Turing ideal I, the degree spectra of families PI and their jumps PI′ are described. For some ideals I generated by c.e. degrees, the spectra of families PI are defined.

AB - Families PI consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps PI′ , are studied. For any countable Turing ideal I, the degree spectra of families PI and their jumps PI′ are described. For some ideals I generated by c.e. degrees, the spectra of families PI are defined.

KW - Turing degree

KW - computable permutation

KW - degree spectra

KW - family of permutations

KW - ideal of Turing degrees

KW - jump

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85178454479&origin=inward&txGid=a8b97f9722ffc66ad9565d154a93b680

UR - https://www.mendeley.com/catalogue/558817c1-ff37-3908-9c78-c9608cf172d2/

U2 - 10.1007/s10469-023-09714-1

DO - 10.1007/s10469-023-09714-1

M3 - Article

VL - 61

SP - 481

EP - 490

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 59388086