TY - JOUR

T1 - Negative Numberings in Admissible Sets. I

AU - Kalimullin, I. Sh

AU - Puzarenko, V. G.

AU - Faĭzrakhmanov, M. Kh

N1 - The work of the first and third authors was partially supported by the Russian Scientific Foundation (project no. 23-21-00181) and was carried out within the framework of the Program for development of the Scientific and Educational Mathematical Center of Volga Federal District (project no. 075-02-2023-944). The work of the second author was partially supported by the Mathematical Center in Akademgorodok (agreement no. 075-15-2022-281 with the Russian Ministry of Science and Higher Education). Публикация для корректировки.

PY - 2023/12

Y1 - 2023/12

N2 - We construct an admissible set \mathbb {A} such thatthe family of all \mathbb {A} -computably enumerable sets possessesa negative computable \mathbb {A} -numbering but lacks positive computable \mathbb {A} -numberings. We also discuss the question on existence of minimal negative \mathbb {A} -numberings.

AB - We construct an admissible set \mathbb {A} such thatthe family of all \mathbb {A} -computably enumerable sets possessesa negative computable \mathbb {A} -numbering but lacks positive computable \mathbb {A} -numberings. We also discuss the question on existence of minimal negative \mathbb {A} -numberings.

KW - admissible set

KW - computable numbering

KW - computable set

KW - computably enumerable set

KW - decidable numbering

KW - negative numbering

KW - numbering

KW - positive numbering

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85179702799&origin=inward&txGid=ba7d0e5979f5ed677efd7f7aae5b1eaf

UR - https://www.mendeley.com/catalogue/54d07f13-ca78-3cc0-86cd-014579d1e63c/

U2 - 10.1134/S105513442304003X

DO - 10.1134/S105513442304003X

M3 - Article

VL - 33

SP - 293

EP - 321

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

ER -