Geodesic
Khutoretskii's theorem for generalized computable families
Algebra i logika, Tome 58 (2019) no. 4, pp. 528-541.

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We give sufficient conditions for generalized computable numberings to satisfy the statement of Khutoretskii's theorem. This implies limitedness of universal $\Sigma^0_\alpha$-computable numberings for $2\leqslant\alpha \omega^{CK}_1$.
Keywords: generalized computable family, generalized computable numbering, Khutoretskii's theorem. 
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M. Kh. Faizrakhmanov. Khutoretskii's theorem for generalized computable families. Algebra i logika, Tome 58 (2019) no. 4, pp. 528-541. http://geodesic.mathdoc.fr/item/AL_2019_58_4_a7/

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