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Matematicheskie Zametki, 2023, Volume 113, Issue 5, Pages 764–774
DOI: https://doi.org/10.4213/mzm13708 (Mi mzm13708) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University
Full-text PDF (562 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm13708
Abstract: The embedding of the first nonconstructive ordinal in the Rogers semilattices of families of arithmetic sets is considered. It is proved that, for any infinite family of arithmetic sets, the first nonconstructive ordinal can be embedded over any minimal element of its Rogers semilattice. It is also shown that if the family is principal or finite, then the first nonconstructive ordinal is embedded over any nongreatest element of its Rogers semilattice.
Keywords: numbering, Rogers semilattice, first nonconstructive ordinal.
Funding agency Grant number
Russian Science Foundation 22-21-20024
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-944
This work was supported by the Russian Science Foundation under grant 22-21-20024, https:// rscf.ru/project/22-21-20024/, and performed in the framework of the realization of the development program of the Scientific-Educational Mathematical Center of Volga Federal Region (contract no. 075-02-2023-944).
Received: 29.08.2022
Revised: 17.10.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 5, Pages 723–730
DOI: https://doi.org/10.1134/S0001434623050127
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 03D45
Language: Russian
Citation: M. Kh. Faizrahmanov, “On the Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices”, Mat. Zametki, 113:5 (2023), 764–774; Math. Notes, 113:5 (2023), 723–730
Citation in format AMSBIB
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\by M.~Kh.~Faizrahmanov
\paper On the Embedding of~the~First Nonconstructive Ordinal
in the Rogers Semilattices
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 5
\pages 764--774
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\crossref{https://doi.org/10.4213/mzm13708}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4602434}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 5
\pages 723--730
\crossref{https://doi.org/10.1134/S0001434623050127}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85163177660}
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    • This publication is cited in the following 1 articles:
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