Numberings on Admissible Structures over Equivalence Relations

Numberings on Admissible Structures over Equivalence Relations Full article

Journal

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Output data

Year: 2024, Volume: 45, Number: 4, Pages: 1833-1840 Pages count : 8 DOI: 10.1134/s1995080224601383

Tags

numberings, decidable numberings, positive numberings, negative numberings, computable numberings, admissible sets.

Authors

Kalimullin I.Sh. ¹ , Puzarenko V.G. ^2,3

Affiliations

1	Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University
2	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
3	Novosibirsk State University

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0012
2	Russian Science Foundation	23-21-00181

Thepapergives aseriesof examplesofadmissiblesets A in whichthe familyof all A-c.e. sets has neither negative, nor positive computable A-numberings. In particular, it is proved that for hereditarily finite superstructures over negative partners of equivalence relations the family of all Σ-subsets may have no negative computable numbering. An opposite result was established earlier for positive numberings and positive partners of equivalence relations [2, 4].

Kalimullin I.S. , Puzarenko V.G.
Numberings on Admissible Structures over Equivalence Relations
Lobachevskii Journal of Mathematics. 2024. V.45. N4. P.1833-1840. DOI: 10.1134/s1995080224601383 WOS Scopus РИНЦ OpenAlex

Submitted:	Jan 20, 2024
Accepted:	Mar 10, 2024
Published print:	Apr 15, 2024
Published online:	Aug 22, 2024

Web of science:	WOS:001422583700038
Scopus:	2-s2.0-85201832611
Elibrary:	68640880
OpenAlex:	W4401810090

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