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 -