Standard

Absolute and Relative Properties of Negatively Numbered Families. / Faizrahmanov, M. Kh; Puzarenko, V. G.

In: Lobachevskii Journal of Mathematics, Vol. 42, No. 4, 6, 04.2021, p. 726-734.

Research output: Contribution to journal › Article › peer-review

Harvard

Faizrahmanov, MK & Puzarenko, VG 2021, 'Absolute and Relative Properties of Negatively Numbered Families', Lobachevskii Journal of Mathematics, vol. 42, no. 4, 6, pp. 726-734. https://doi.org/10.1134/S1995080221040090

APA

Faizrahmanov, M. K., & Puzarenko, V. G. (2021). Absolute and Relative Properties of Negatively Numbered Families. Lobachevskii Journal of Mathematics, 42(4), 726-734. [6]. https://doi.org/10.1134/S1995080221040090

Vancouver

Faizrahmanov MK, Puzarenko VG. Absolute and Relative Properties of Negatively Numbered Families. Lobachevskii Journal of Mathematics. 2021 Apr;42(4):726-734. 6. doi: 10.1134/S1995080221040090

Author

Faizrahmanov, M. Kh ; Puzarenko, V. G. / Absolute and Relative Properties of Negatively Numbered Families. In: Lobachevskii Journal of Mathematics. 2021 ; Vol. 42, No. 4. pp. 726-734.

BibTeX

@article{74f3b919703444f3964dd7b26e73cbd8,
title = "Absolute and Relative Properties of Negatively Numbered Families",
abstract = "We study in this paper negative A-numberings where A are admissible structures. We establish that a series of classical assumptions is remained to hold for negative A-numberings in the case of the application of certain limits as for numberings as for admissible structures. We find examples of admissible structures A whose families of all Σ-subsets have negative non-decidable minimal computable A-numberings. The admissible structures from this series have negative computable A-numberings whose numbered equivalence differs from corresponding ones of any computable A-numbering of family of total functions.",
keywords = "admissible structure, analytic hierarchy, equivalence, hyperarithmetical sets, minimal numbering, negative numbering, numbering",
author = "Faizrahmanov, {M. Kh} and Puzarenko, {V. G.}",
note = "Funding Information: The first author was supported by the Russian Science Foundation, project no. 18-11-00028. The second author was supported by the Russian Science Foundation, project no. 18-11-00028 and the State Task to the Sobolev Institute of Mathematics, project no. 0314-2019-0003. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = apr,
doi = "10.1134/S1995080221040090",
language = "English",
volume = "42",
pages = "726--734",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "4",

}

RIS

TY - JOUR

T1 - Absolute and Relative Properties of Negatively Numbered Families

AU - Faizrahmanov, M. Kh

AU - Puzarenko, V. G.

N1 - Funding Information: The first author was supported by the Russian Science Foundation, project no. 18-11-00028. The second author was supported by the Russian Science Foundation, project no. 18-11-00028 and the State Task to the Sobolev Institute of Mathematics, project no. 0314-2019-0003. Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/4

Y1 - 2021/4

N2 - We study in this paper negative A-numberings where A are admissible structures. We establish that a series of classical assumptions is remained to hold for negative A-numberings in the case of the application of certain limits as for numberings as for admissible structures. We find examples of admissible structures A whose families of all Σ-subsets have negative non-decidable minimal computable A-numberings. The admissible structures from this series have negative computable A-numberings whose numbered equivalence differs from corresponding ones of any computable A-numbering of family of total functions.

AB - We study in this paper negative A-numberings where A are admissible structures. We establish that a series of classical assumptions is remained to hold for negative A-numberings in the case of the application of certain limits as for numberings as for admissible structures. We find examples of admissible structures A whose families of all Σ-subsets have negative non-decidable minimal computable A-numberings. The admissible structures from this series have negative computable A-numberings whose numbered equivalence differs from corresponding ones of any computable A-numbering of family of total functions.

KW - admissible structure

KW - analytic hierarchy

KW - equivalence

KW - hyperarithmetical sets

KW - minimal numbering

KW - negative numbering

KW - numbering

UR - http://www.scopus.com/inward/record.url?scp=85107363664&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=45684035

UR - https://www.mendeley.com/catalogue/87fab623-be88-3374-8fee-b58912283db5/

U2 - 10.1134/S1995080221040090

DO - 10.1134/S1995080221040090

M3 - Article

AN - SCOPUS:85107363664

VL - 42

SP - 726

EP - 734

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 4

M1 - 6

ER -

ID: 28886706