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This article is cited in 2 scientific papers (total in 2 papers)
Mathematics
Two theorems on minimal generally-computable numberings
M. Kh. Faizrahmanov Scientific-Educational Mathematical Center of Volga Federal District
Abstract:
The paper proves that for any set $A$ that computes a non-computable computably enumerable set, any infinite $A$-computable family has an infinite number of pairwise nonequivalent minimal $A$-computable numberings. It is established that an arbitrary set $A\leqslant_T\emptyset '$ is low if and only if any infinite $A$-computable family with the greatest set under inclusion has an infinite number of pairwise nonequivalent positive $A$-computable numberings.
Key words:
minimal numbering, positive numbering, computably enumerable set, low set.
Received: 14.11.2022
Citation:
M. Kh. Faizrahmanov, “Two theorems on minimal generally-computable numberings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 3, 28–35; Moscow University Mathematics Bulletin, 78:3 (2023), 136–143
Linking options:
https://www.mathnet.ru/eng/vmumm4537 https://www.mathnet.ru/eng/vmumm/y2023/i3/p28
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Abstract page: | 145 | Full-text PDF : | 60 | References: | 31 |
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