Standard

Computable Positive and Friedberg Numberings in Hyperarithmetic. / Kalimullin, I. Sh; Puzarenko, V. G.; Faizrakhmanov, M. Kh.

In: Algebra and Logic, Vol. 59, No. 1, 01.03.2020, p. 46-58.

Research output: Contribution to journal › Article › peer-review

Harvard

Kalimullin, IS, Puzarenko, VG & Faizrakhmanov, MK 2020, 'Computable Positive and Friedberg Numberings in Hyperarithmetic', Algebra and Logic, vol. 59, no. 1, pp. 46-58. https://doi.org/10.1007/s10469-020-09578-9

APA

Kalimullin, I. S., Puzarenko, V. G., & Faizrakhmanov, M. K. (2020). Computable Positive and Friedberg Numberings in Hyperarithmetic. Algebra and Logic, 59(1), 46-58. https://doi.org/10.1007/s10469-020-09578-9

Vancouver

Kalimullin IS, Puzarenko VG, Faizrakhmanov MK. Computable Positive and Friedberg Numberings in Hyperarithmetic. Algebra and Logic. 2020 Mar 1;59(1):46-58. doi: 10.1007/s10469-020-09578-9

Author

Kalimullin, I. Sh ; Puzarenko, V. G. ; Faizrakhmanov, M. Kh. / Computable Positive and Friedberg Numberings in Hyperarithmetic. In: Algebra and Logic. 2020 ; Vol. 59, No. 1. pp. 46-58.

BibTeX

@article{fe760aca7a74456ea0870dc0014f64c8,
title = "Computable Positive and Friedberg Numberings in Hyperarithmetic",
abstract = "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.",
keywords = "admissible set, analytical hierarchy, computable numbering, Friedberg numbering, negative numbering, positive numbering, FAMILIES, PRESENTATIONS",
author = "Kalimullin, {I. Sh} and Puzarenko, {V. G.} and Faizrakhmanov, {M. Kh}",
year = "2020",
month = mar,
day = "1",
doi = "10.1007/s10469-020-09578-9",
language = "English",
volume = "59",
pages = "46--58",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "1",

}

RIS

TY - JOUR

T1 - Computable Positive and Friedberg Numberings in Hyperarithmetic

AU - Kalimullin, I. Sh

AU - Puzarenko, V. G.

AU - Faizrakhmanov, M. Kh

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - admissible set

KW - analytical hierarchy

KW - computable numbering

KW - Friedberg numbering

KW - negative numbering

KW - positive numbering

KW - FAMILIES

KW - PRESENTATIONS

UR - http://www.scopus.com/inward/record.url?scp=85087002640&partnerID=8YFLogxK

U2 - 10.1007/s10469-020-09578-9

DO - 10.1007/s10469-020-09578-9

M3 - Article

AN - SCOPUS:85087002640

VL - 59

SP - 46

EP - 58

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -

ID: 24615904