Geodesic
Some Properties of Numberings in Various Levels in Ershov's Hierarchy
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 125-132

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There was proved, that there no $\Delta^{-1}_{a}$-computable numbering of family of all $\Delta^{-1}_{a}$-sets, $a$ is constructive ordinal. Also there was proved, that there is minimal $\omega$-computable numbering of family of all sets from $\bigcup\limits_{k\in\omega}\Sigma_{k}^{-1}$.
Keywords: computable numbering, friedberg numbering, Ershov's hierarchy. 
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     author = {S. S. Ospichev},
     title = {Some {Properties} of {Numberings} in {Various} {Levels} in {Ershov's} {Hierarchy}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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S. S. Ospichev. Some Properties of Numberings in Various Levels in Ershov's Hierarchy. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 125-132. http://geodesic.mathdoc.fr/item/VNGU_2010_10_4_a8/