Abstract
In this paper we consider the completeness criteria for a class of sub-Turing reducibilities.
REFERENCES
R. I. Soare, Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, Perspectives in Mathematical Logic (Springer, Berlin, 1987).
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
M. M. Arslanov, “Completeness in the arithmetical hierarchy and fixed points,” Algebra Logic 28 (1), 1–9 (1989). https://doi.org/10.1007/BF01980603
M. M. Arslanov, “Some generalizations of a fixed-point theorem,” Sov. Math. 25 (5), 1–10 (1981).
V. D. Solov’ev, “Some generalizations of the notions of reducibility and creativity,” Sov. Math. 20 (3), 56–62 (1976).
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
V. K. Bulitko, “On ways of characterizing complete sets,” Math. USSR-Izv. 38 (2), 225–250 (1992). https://doi.org/10.1070/IM1992v038n02ABEH002197
A. N. Degtev, Recursively Enumerable Sets and Reducibility of Truth-Table Type (Nauka, Moscow, 1998) [in Russian].
V. K. Bulitko, “Letter to the editor,” Izv.: Math. 41 (4), 185 (1993).
J. Myhill, “Creative sets,” Z. Math. Logik Grundlagen Math. 1 (2), 97 –108 (1955). https://doi.org/10.1002/malq.19550010205
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
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X22100012