Email this article Some Absolute Properties of A-Computable Numberings
- Authors: Badaev S.A.1, Issakhov A.A.1,2
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Affiliations:
- Al-Farabi Kazakh National University
- Kazkh-British Technical University
- Issue: Vol 57, No 4 (2018)
- Pages: 275-288
- Section: Article
- URL: https://journals.rcsi.science/0002-5232/article/view/234094
- DOI: https://doi.org/10.1007/s10469-018-9499-0
- ID: 234094
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Abstract
For an arbitrary set A of natural numbers, we prove the following statements: every finite family of A-computable sets containing a least element under inclusion has an Acomputable universal numbering; every infinite A-computable family of total functions has (up to A-equivalence) either one A-computable Friedberg numbering or infinitely many such numberings; every A-computable family of total functions which contains a limit function has no A-computable universal numberings, even with respect to Areducibility.
About the authors
S. A. Badaev
Al-Farabi Kazakh National University
Author for correspondence.
Email: Serikzhan.Badaev@kaznu.kz
Kazakhstan, Al-Farabi Ave. 71, Alma-Ata, 050040
A. A. Issakhov
Al-Farabi Kazakh National University; Kazkh-British Technical University
Author for correspondence.
Email: asylissakhov@gmail.com
Kazakhstan, Al-Farabi Ave. 71, Alma-Ata, 050040; ul. Tole bi 59, Alma-Ata, 050000
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