Some Properties of Numberings in Various Levels in Ershov's Hierarchy

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 $\bigcup\limits_{k\in\omega}\Sigma_{k}^{-1}$.