Abstract
It is proved that there exist infinitely many positive undecidable Σ -1 n -computable numberings of every infinite family \(S \subseteq \Sigma _n^{ - 1}\) that admits at least one Σ -1 n -computable numbering and contains either the empty set, for even n, or N for odd n.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Yu. L. Ershov, Numeration Theory [in Russian], Nauka, Moscow (1977).
A. I. Mal'tsev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).
H. Rogers, Theory of Recursive Functions and Effective Computa»ility, McGraw-Hill, New York (1967).
S. S. Goncharov and A. Sor»i, “Generalized computa»le numerations and nontrivial Rogers semilattices, ” Alge»ra Logika, 36, No. 6, 621–641 (1997).
Yu. L. Ershov, “A hierarchy of sets I, ” Alge»ra Logika, 7, No. 1, 47–74 (1968).
A. I. Mal'tsev, “Positive and negative enumerations, ” Dokl. Akad. Nauk SSSR, 160, No. 2, 243–256 (1969).
S. A. Badaev and S. S. Goncharov, “Theory of num»erings. Open pro»lems, ” in Computa»ility Theory and Its Applications, Current Trends and Open Pro»lems, Cont. Math., Vol. 257, Am. Math. Soc., Providence, RI (2000), pp. 23–38.
Zh. T. Talas»aeva, “Positive computa»ility of a family of ∑ —1n -sets, ” Proc. 54th Students and Young Scientists' Conference, KazGNU, Almaty (2000), pp. 145–148.
S. A. Badaev, “Positive enumerations, ” Si». Mat. Zh., 18, No. 3, 483–496 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Talasbaeva, Z.T. Positive Numberings of Families of Sets in the Ershov Hierarchy. Algebra and Logic 42, 413–418 (2003). https://doi.org/10.1023/B:ALLO.0000004175.64588.32
Issue Date:
DOI: https://doi.org/10.1023/B:ALLO.0000004175.64588.32