On Universal Pairs in the Ershov Hierarchy

Abstract

We develop the Ershov theory of C-classes for some finite families of sets in the Ershov hierarchy. We generalize the result by Muchnik on multiple \( m \)-reducibility as follows: There exists an \( m \)-universal pair of disjoint sets for each level of the Ershov hierarchy.

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Funding

N. A. Bazhenov and S. S. Ospichev were supported by the Mathematical Center in Akademgorodok (Agreement 075–15–2019–1613 with the Ministry of Science and Higher Education). M. Mustafa was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342 and partially supported by the MES RK Grant AP08856834.

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Correspondence to N. A. Bazhenov.

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To the memory of Sergei Yur’evich Podzorov.

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Cite this article

Bazhenov, N.A., Mustafa, M. & Ospichev, S.S. On Universal Pairs in the Ershov Hierarchy. Sib Math J 62, 23–31 (2021). https://doi.org/10.1134/S0037446621010031

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Keywords

  • Ershov hierarchy
  • \( m \)-reducibility
  • C-class
  • computable numbering

UDC

  • 510.55