Geodesic
Families of permutations and ideals of Turing degrees
Algebra i logika, Tome 61 (2022) no. 6, pp. 706-719

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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. 
@article{AL_2022_61_6_a3,
     author = {A. S. Morozov and V. G. Puzarenko and M. Kh. Faizrahmanov},
     title = {Families of permutations and ideals of {Turing} degrees},
     journal = {Algebra i logika},
     pages = {706--719},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2022_61_6_a3/}
}
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A. S. Morozov; V. G. Puzarenko; M. Kh. Faizrahmanov. Families of permutations and ideals of Turing degrees. Algebra i logika, Tome 61 (2022) no. 6, pp. 706-719. http://geodesic.mathdoc.fr/item/AL_2022_61_6_a3/