Computable Positive and Friedberg Numberings in Hyperarithmetic

Computable Positive and Friedberg Numberings in Hyperarithmetic Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2020, Volume: 59, Number: 1, Pages: 46-58 Pages count : 13 DOI: 10.1007/s10469-020-09578-9

Tags

admissible set; analytical hierarchy; computable numbering; Friedberg numbering; negative numbering; positive numbering

Authors

Kalimullin I.S. ¹ , Puzarenko V.G. ^2,3 , Faizrakhmanov M.K. ¹

Affiliations

1	Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008, Russian Federation
2	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russian Federation

We point out an existence criterion for positive computable total Π11 -numberings of families of subsets of a given Π11 -set. In particular, it is stated that the family of all Π11 -sets has no positive computable total Π11 -numberings. Also we obtain a criterion of existence for computable Friedberg Σ11 -numberings of families of subsets of a given Σ11 - set, the consequence of which is the absence of a computable Friedberg Σ11 -numbering of the family of all Σ11 -sets. Questions concerning the existence of negative computable Π11 - and Σ11 -numberings of the families mentioned are considered. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Kalimullin I.S. , Puzarenko V.G. , Faizrakhmanov M.K.
Computable Positive and Friedberg Numberings in Hyperarithmetic
Algebra and Logic. 2020. V.59. N1. P.46-58. DOI: 10.1007/s10469-020-09578-9 WOS Scopus OpenAlex

Калимуллин И.Ш. , Пузаренко В.Г. , Файзрахманов М.Х.
О позитивных и однозначных нумерациях в гиперарифметике
Алгебра и логика. 2020. Т.59. №1. С.66-83. DOI: 10.33048/alglog.2020.59.104 OpenAlex

Web of science:	WOS:000534860600002
Scopus:	2-s2.0-85087002640
OpenAlex:	W3026799064

DB	Citing
Scopus	3
OpenAlex	3
Web of science	2