M. Kh. Faizrahmanov, “Minimal generalized computable enumerations and high degrees”, Sibirsk. Mat. Zh., 58:3 (2017), 710–716; Siberian Math. J., 58:3 (2017), 553

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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 3, Pages 710–716
DOI: https://doi.org/10.17377/smzh.2017.58.318 (Mi smj2891)

This article is cited in 13 scientific papers (total in 13 papers)

Minimal generalized computable enumerations and high degrees

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, Kazan, Russia

Full-text PDF (287 kB) Citations (13)

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DOI: https://doi.org/10.17377/smzh.2017.58.318

Abstract: We establish that the set of minimal generalized computable enumerations of every infinite family computable with respect to a high oracle is effectively infinite. We find some sufficient condition for enumerations of the infinite families computable with respect to high oracles under which there exist minimal generalized computable enumerations that are irreducible to the enumerations.

Keywords: generalized computable enumeration, minimal enumeration, high set, Low$_2$ set, arithmetic enumeration.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation	1.1515.2017/ПЧ
Russian Foundation for Basic Research	15-01-08252
The author was supported by the subsidy of the government task for Kazan (Volga Region) Federal University (Grant 1.1515.2017/PP) and the Russian Foundation for Basic Research (Grant 15-01-08252).

Received: 03.03.2016
Revised: 13.12.2016

English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 3, Pages 553–558
DOI: https://doi.org/10.1134/S0037446617030181

Bibliographic databases:

Document Type: Article

UDC: 510.54+510.57

MSC: 35R30

Language: Russian

Citation: M. Kh. Faizrahmanov, “Minimal generalized computable enumerations and high degrees”, Sibirsk. Mat. Zh., 58:3 (2017), 710–716; Siberian Math. J., 58:3 (2017), 553–558

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Linking options:

https://www.mathnet.ru/eng/smj2891

https://www.mathnet.ru/eng/smj/v58/i3/p710

This publication is cited in the following 13 articles:

Sh. D. Nodirov, M. Kh. Faizrahmanov, “Some properties of classes of minimal numberings of arithmetical set families”, jour, 2:1 (2024), 94
Marat Faizrahmanov, “On Non-principal Arithmetical Numberings and Families”, Theory Comput Syst, 68:2 (2024), 271
M. Kh. Faizrahmanov, “A Family with a Single Minimal but Not Least Numbering”, Sib Math J, 65:2 (2024), 381
M. Kh. Faizrakhmanov, “Semeistvo s edinstvennoi minimalnoi, no ne naimenshei numeratsiei”, Sib. matem. zhurn., 65:2 (2024), 395–407
M. Kh. Faizrahmanov, “On the Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices”, Math. Notes, 113:5 (2023), 723–730
M. Kh. Faizrakhmanov, “Effektivno beskonechnye klassy numeratsii vychislimykh semeistv deistvitelnykh chisel”, Izv. vuzov. Matem., 2023, no. 5, 96–100
M. Kh. Faizrahmanov, “Two theorems on minimal generally-computable numberings”, Moscow University Mathematics Bulletin, 78:3 (2023), 136–143
M. Kh. Faizrahmanov, “Effectively Infinite Classes of Numberings of Computable Families of Reals”, Russ Math., 67:5 (2023), 72
M. Kh. Faizrahmanov, “On $p$-universal and $p$-minimal numberings”, Siberian Math. J., 63:2 (2022), 365–373
Marat Faizrahmanov, “Extremal numberings and fixed point theorems”, Mathematical Logic Qtrly, 68:4 (2022), 398
Z. K. Ivanova, M. Kh. Faizrahmanov, “Weak reducibility of computable and generalized computable numberings”, Sib. elektron. matem. izv., 18:1 (2021), 112–120
I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Positive presentations of families relative to $e$-oracles”, Siberian Math. J., 59:4 (2018), 648–656
M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Siberian Math. J., 58:6 (2017), 1104–1110

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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