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. 
@article{AL_2019_58_4_a7,
     author = {M. Kh. Faizrakhmanov},
     title = {Khutoretskii's theorem for generalized computable families},
     journal = {Algebra i logika},
     pages = {528--541},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_4_a7/}
}
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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/