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 -