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Khutoretskii’s Theorem for Generalized Computable Families

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Algebra and Logic Aims and scope

We give sufficient conditions for generalized computable numberings to satisfy the statement of Khutoretskii’s theorem. This implies limitedness of universal \( {\varSigma}_{\alpha}^0- \) computable numberings for 2 \( \le \alpha <{\omega}_1^{CK}. \)

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008, Russia

    M. Kh. Faizrakhmanov

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  1. M. Kh. Faizrakhmanov
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Correspondence to M. Kh. Faizrakhmanov.

Additional information

The work was carried out at the expense of the subsidy allocated to Kazan (Volga Region) Federal University for the fulfillment of the state task in the sphere of scientific activity, project No. 1.1515.2017/4.6.

Translated from Algebra i Logika, Vol. 58, No. 4, pp. 528-541, July-August, 2019.

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Faizrakhmanov, M.K. Khutoretskii’s Theorem for Generalized Computable Families. Algebra Logic 58, 356–365 (2019). https://doi.org/10.1007/s10469-019-09557-9

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  • DOI: https://doi.org/10.1007/s10469-019-09557-9

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