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Algebra Logika, 2019 Volume 58, Number 4, Pages 528–541 (Mi al914)

This article is cited in 10 papers

Khutoretskii's theorem for generalized computable families

M. Kh. Faizrakhmanov

Kazan (Volga Region) Federal University

Abstract: 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.

UDC: 510.5

Received: 20.04.2018
Revised: 08.11.2019

DOI: 10.33048/alglog.2019.58.408


 English version:
Algebra and Logic, 2019, 58:4, 356–365

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© Steklov Math. Inst. of RAS, 2025