Geodesic
Universal generalized computable numberings and hyperimmunity
Algebra i logika, Tome 56 (2017) no. 4, pp. 506-521

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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.
Keywords: generalized computable numbering, universal numbering, precomplete numbering, hyperimmune set, high set. 
@article{AL_2017_56_4_a7,
     author = {M. Kh. Faizrakhmanov},
     title = {Universal generalized computable numberings and hyperimmunity},
     journal = {Algebra i logika},
     pages = {506--521},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_4_a7/}
}
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M. Kh. Faizrakhmanov. Universal generalized computable numberings and hyperimmunity. Algebra i logika, Tome 56 (2017) no. 4, pp. 506-521. http://geodesic.mathdoc.fr/item/AL_2017_56_4_a7/