INFINITE FAMILIES OF TOTAL FUNCTIONS WITH PRINCIPAL NUMBERINGS
https://doi.org/10.55452/1998-6688-2021-18-2-53-58
Abstract
It was known that any non-single-element (in particular, any infinite) family of total functions with an oracle A, such that Ø′≤TA, does not have A-computable principal numbering; later it was proved that any finite family of total functions with a hyperimmune-free oracle A always has an A-computable principal numbering. The unresolved question was whether there exists an infinite family of total functions with a hyperimmune-free oracle A that has an A-computable principal numbering. The paper gives a positive answer to this question: it is proved that there exists an infinite A-computable family F of total functions, where the Turing degree of the set A is hyperimmune-free, such that F has an A-computable principal numbering.
Supporting agencies: This work was supported by the Science Committee of the Republic of Kazakhstan (Grant AP08856493).
About the Authors
A. A. Issakhov
Kazakh-British technical university
Kazakhstan
Kazakhstan
Assylbek A. Issakhov - PhD Doctor, Head and Professor of the Scientific and Educational Center of Mathematics and Cybernetics
050000, Almaty
F. Rakymzhankyzy
Kazakh-British technical university
Kazakhstan
Kazakhstan
Fariza Rakymzhankyzy - Master of Science, PhD student, Scientific and Educational Center for Mathematics and Cybernetics
050000, Almaty
U. Ostemirova
Kazakh-British technical university
Kazakhstan
Kazakhstan
Uldana B. Ostemirova – PhD student, tutor of the Scientific and Educational Center of Mathematics and Cybernetics
050000, Almaty
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Review
For citations:
Issakhov A.A., Rakymzhankyzy F., Ostemirova U. INFINITE FAMILIES OF TOTAL FUNCTIONS WITH PRINCIPAL NUMBERINGS. Herald of the Kazakh-British technical university. 2021;18(2):53-58. https://doi.org/10.55452/1998-6688-2021-18-2-53-58
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