TY - JOUR

T1 - Numberings on Admissible Structures over Equivalence Relations

AU - Kalimullin, I. Sh

AU - Puzarenko, V. G.

N1 - The work of I.Sh. Kalimullin is supported by the Russian Science Foundation (grant no. 23-21-00181) and performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2023-944). The work of V.G. Puzarenko is supported by project FWNF-2022-0012 (Classification Aspects of Syntax and Semantic of Logical Systems).

PY - 2024/4

Y1 - 2024/4

N2 - Abstract: The paper gives a series of examples of admissible sets in which the family of all -c.e. sets has neither negative, nor positive computable -numberings. In particular, it is proved that for hereditarily finite superstructures over negative partners of equivalence relations the family of all -subsets may have no negative computable numbering. An opposite result was established earlier for positive numberings and positive partners of equivalence relations [2, 4].

AB - Abstract: The paper gives a series of examples of admissible sets in which the family of all -c.e. sets has neither negative, nor positive computable -numberings. In particular, it is proved that for hereditarily finite superstructures over negative partners of equivalence relations the family of all -subsets may have no negative computable numbering. An opposite result was established earlier for positive numberings and positive partners of equivalence relations [2, 4].

KW - admissible sets

KW - computable numberings

KW - decidable numberings

KW - negative numberings

KW - numberings

KW - positive numberings

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85201832611&origin=inward&txGid=ff123a50c84219dce90e178e249629fe

UR - https://www.mendeley.com/catalogue/2b89d86b-67fb-3027-b106-ed1075f0813d/

U2 - 10.1134/S1995080224601383

DO - 10.1134/S1995080224601383

M3 - Article

VL - 45

SP - 1833

EP - 1840

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 4

ER -