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Turing jumps in the Ershov hierarchy

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Algebra and Logic Aims and scope

We look at infinite levels of the Ershov hierarchy in the natural system of notation, which are proper for jumps of sets. It is proved that proper infinite levels for jumps are confined to \( \Delta_a^{ - 1} \) -levels, where a stands for an ordinal ωn > 1.

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Authors and Affiliations

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

    M. Kh. Faizrakhmanov

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

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Supported by RFBR (project Nos. 09-01-97010, 10-01-00399, MK-1784.2010.1), by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” (gov. contracts P267 and 14.740.11.1142), and by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1/5367).

Translated from Algebra i Logika, Vol. 50, No. 3, pp. 399–414, May-June, 2011.

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Faizrakhmanov, M.K. Turing jumps in the Ershov hierarchy. Algebra Logic 50, 279–289 (2011). https://doi.org/10.1007/s10469-011-9141-x

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  • DOI: https://doi.org/10.1007/s10469-011-9141-x

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