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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 6, Pages 1418–1427
DOI: https://doi.org/10.17377/smzh.2017.58.619
(Mi smj2948)
 

This article is cited in 9 scientific papers (total in 9 papers)

The Rogers semilattices of generalized computable enumerations

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan, Russia
Full-text PDF (303 kB) Citations (9)
References:
Abstract: We study the cardinality and structural properties of the Rogers semilattice of generalized computable enumerations with arbitrary noncomputable oracles and oracles of hyperimmune Turing degree. We show the infinity of the Rogers semilattice of generalized computable enumerations of an arbitrary nontrivial family with a noncomputable oracle. In the case of oracles of hyperimmune degree we prove that the Rogers semilattice of an arbitrary infinite family includes an ideal without minimal elements and establish that the top, if present, is a limit element under the condition that the family contains the inclusion-least set.
Keywords: computable enumeration, generalized computable enumeration, Rogers semilattice, hyperimmune set, minimal enumeration, universal enumeration.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.1515.2017/4.6
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 1.1515.2017/4.6) and the Russian Foundation for Basic Research (Grant 15-01-08252).
Received: 16.11.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 6, Pages 1104–1110
DOI: https://doi.org/10.1134/S0037446617060192
Bibliographic databases:
Document Type: Article
UDC: 510.57
MSC: 35R30
Language: Russian
Citation: M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Sibirsk. Mat. Zh., 58:6 (2017), 1418–1427; Siberian Math. J., 58:6 (2017), 1104–1110
Citation in format AMSBIB
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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