Skip to main content
Log in

Completeness Criteria for a Class of Reducibilities

  • BRIEF COMMUNICATION
  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

In this paper we consider the completeness criteria for a class of sub-Turing reducibilities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  1. R. I. Soare, Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, Perspectives in Mathematical Logic (Springer, Berlin, 1987).

    Book  MATH  Google Scholar 

  2. M. M. Arslanov, “Truth–table complete computably enumerable sets,” in Computability and Models, Ed. by S. B. Cooper and S. S. Goncharov, The University Series in Mathematics (Springer, New York, 2020), pp. 1–10. https://doi.org/10.1007/978-1-4615-0755-0_1

  3. M. M. Arslanov, “Completeness in the arithmetical hierarchy and fixed points,” Algebra Logic 28 (1), 1–9 (1989). https://doi.org/10.1007/BF01980603

    Article  MathSciNet  MATH  Google Scholar 

  4. M. M. Arslanov, “Some generalizations of a fixed-point theorem,” Sov. Math. 25 (5), 1–10 (1981).

    MATH  Google Scholar 

  5. V. D. Solov’ev, “Some generalizations of the notions of reducibility and creativity,” Sov. Math. 20 (3), 56–62 (1976).

    MATH  Google Scholar 

  6. I. I. Batyrshin, “Quasi-completeness and functions without fixed-points,” Math. Logic Q. 52 (6), 595–601 (2006). https://doi.org/10.1002/malq.200610017

    Article  MathSciNet  MATH  Google Scholar 

  7. V. K. Bulitko, “On ways of characterizing complete sets,” Math. USSR-Izv. 38 (2), 225–250 (1992). https://doi.org/10.1070/IM1992v038n02ABEH002197

    Article  MATH  Google Scholar 

  8. A. N. Degtev, Recursively Enumerable Sets and Reducibility of Truth-Table Type (Nauka, Moscow, 1998) [in Russian].

    MATH  Google Scholar 

  9. V. K. Bulitko, “Letter to the editor,” Izv.: Math. 41 (4), 185 (1993).

    Article  Google Scholar 

  10. J. Myhill, “Creative sets,” Z. Math. Logik Grundlagen Math. 1 (2), 97 –108 (1955). https://doi.org/10.1002/malq.19550010205

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This study was supported by a grant from the Russian Science Foundation (project no. 22-21-20024) and carried out as part of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District (agreement no. 075-02-2022-882).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. M. Arslanov.

Ethics declarations

The author declares that he has no conflicts of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arslanov, M.M. Completeness Criteria for a Class of Reducibilities. Russ Math. 66, 62–66 (2022). https://doi.org/10.3103/S1066369X22100012

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X22100012

Keywords:

Navigation