Abstract:
Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for generalized computable numberings to be precomplete. In addition, we look into the question on boundedness of universal numberings computable relative to high oracles.
The work was carried out at the expense of the subsidy allocated to Kazan (Volga Region) Federal University
for the fulfillment of the state task in the sphere of scientific activity (project No. 1.1515.2017/4.6) and supported
by RFBR (project No. 15-01-08252).
This publication is cited in the following 12 articles:
Marat Faizrahmanov, “Some properties of precompletely and positively numbered sets”, Annals of Pure and Applied Logic, 176:2 (2025), 103523
N. K. Kasymov, “Locally finite and finitely approximated unoids over computably separable equivalences”, jour, 2:1 (2024), 55
M. Kh. Faizrahmanov, “On $e$-principal and $e$-complete numberings”, Math. Notes, 116:3 (2024), 541–553
M. Kh. Faizrahmanov, “On $p$-universal and $p$-minimal numberings”, Siberian Math. J., 63:2 (2022), 365–373
F. Rakymzhankyzy, N. A. Bazhenov, A. A. Isakhov, B. S. Kalmurzaev, “Minimalnye obobschenno vychislimye numeratsii i semeistva pozitivnykh predporyadkov”, Algebra i logika, 61:3 (2022), 280–307
F. Rakymzhankyzy, N. A. Bazhenov, A. A. Issakhov, B. S. Kalmurzayev, “Minimal Generalized Computable Numberings and Families of Positive Preorders”, Algebra Logic, 61:3 (2022), 188
Marat Faizrahmanov, “Extremal numberings and fixed point theorems”, Mathematical Logic Qtrly, 68:4 (2022), 398
Z. K. Ivanova, M. Kh. Faizrahmanov, “Weak reducibility of computable and generalized computable numberings”, Sib. elektron. matem. izv., 18:1 (2021), 112–120
M. Kh. Faizrakhmanov, “Khutoretskii's theorem for generalized computable families”, Algebra and Logic, 58:4 (2019), 356–365
M. Kh. Faizrakhmanov, “Reshetochnye svoistva polureshetok Rodzhersa vychislimykh i obobschenno vychislimykh semeistv”, Sib. elektron. matem. izv., 16 (2019), 1927–1936
I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Positive presentations of families relative to $e$-oracles”, Siberian Math. J., 59:4 (2018), 648–656
S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra and Logic, 57:4 (2018), 275–288
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