Geodesic
Positive Numberings of Families of Sets in the Ershov Hierarchy
Algebra i logika, Tome 42 (2003) no. 6, pp. 737-746

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It is proved that there exist infinitely many positive undecidable $\Sigma^{-1}_n$-computable numberings of every infinite family $\mathcal S\subseteq\Sigma^{-1}_n$ that admits at least one $\Sigma^{-1}_n$-computable numbering and contains either the empty set, for even $n$, or $N$ for odd $n$.
Keywords: Ershov hierarchy, positive undecidable $\Sigma^{-1}_n$-computable numbering. 
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     author = {Zh. T. Talasbaeva},
     title = {Positive {Numberings} of {Families} of {Sets} in the {Ershov} {Hierarchy}},
     journal = {Algebra i logika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_6_a6/}
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Zh. T. Talasbaeva. Positive Numberings of Families of Sets in the Ershov Hierarchy. Algebra i logika, Tome 42 (2003) no. 6, pp. 737-746. http://geodesic.mathdoc.fr/item/AL_2003_42_6_a6/