Geodesic
Decidable Computable $\mathbb A$-Numberings
Algebra i logika, Tome 41 (2002) no. 5, pp. 568-584.

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The article deals in the numbering theory for admissible sets, brought in sight in [1]. For models of two special classes, we resolve the problem of there being 1-1 computable numberings of the families of all computable sets and of all computable functions. In proofs, for the former case the role of finite objects is played by syntactic constructions, and for the latter – by finite subsets on hereditarily finite superstructures.
Mots-clés : admissible set
Keywords: numbering. 
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     author = {V. G. Puzarenko},
     title = {Decidable {Computable} $\mathbb A${-Numberings}},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
     volume = {41},
     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_5_a3/}
}
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V. G. Puzarenko. Decidable Computable $\mathbb A$-Numberings. Algebra i logika, Tome 41 (2002) no. 5, pp. 568-584. http://geodesic.mathdoc.fr/item/AL_2002_41_5_a3/

[1] Yu. L. Ershov, Opredelimost i vychislimost, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR | Zbl

[2] V. G. Puzarenko, “O vychislimosti nad modelyami razreshimykh teorii”, Algebra i logika, 39:2 (2000), 170–197 | MR | Zbl

[3] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR

[4] A. I. Maltsev, Algoritmy i rekursivnye funktsii, Nauka, M., 1986 | MR