Standard

Computable Numberings of Families of Infinite Sets. / Dorzhieva, M. V.

In: Algebra and Logic, Vol. 58, No. 3, 01.07.2019, p. 224-231.

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

Harvard

Dorzhieva, MV 2019, 'Computable Numberings of Families of Infinite Sets', Algebra and Logic, vol. 58, no. 3, pp. 224-231. https://doi.org/10.1007/s10469-019-09540-4

APA

Dorzhieva, M. V. (2019). Computable Numberings of Families of Infinite Sets. Algebra and Logic, 58(3), 224-231. https://doi.org/10.1007/s10469-019-09540-4

Vancouver

Dorzhieva MV. Computable Numberings of Families of Infinite Sets. Algebra and Logic. 2019 Jul 1;58(3):224-231. doi: 10.1007/s10469-019-09540-4

Author

Dorzhieva, M. V. / Computable Numberings of Families of Infinite Sets. In: Algebra and Logic. 2019 ; Vol. 58, No. 3. pp. 224-231.

BibTeX

@article{8452c3a72b7f4fbf955ad61cb979a50b,
title = "Computable Numberings of Families of Infinite Sets",
abstract = "We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.",
keywords = "analytical hierarchy, computability, computable numberings, Friedberg numbering, G{\"o}del{\textquoteright}s axiom of constructibility, Godel's axiom of constructibility, AXIOM",
author = "Dorzhieva, {M. V.}",
year = "2019",
month = jul,
day = "1",
doi = "10.1007/s10469-019-09540-4",
language = "English",
volume = "58",
pages = "224--231",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "3",

}

RIS

TY - JOUR

T1 - Computable Numberings of Families of Infinite Sets

AU - Dorzhieva, M. V.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.

AB - We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.

KW - analytical hierarchy

KW - computability

KW - computable numberings

KW - Friedberg numbering

KW - Gödel’s axiom of constructibility

KW - Godel's axiom of constructibility

KW - AXIOM

UR - http://www.scopus.com/inward/record.url?scp=85074822859&partnerID=8YFLogxK

U2 - 10.1007/s10469-019-09540-4

DO - 10.1007/s10469-019-09540-4

M3 - Article

AN - SCOPUS:85074822859

VL - 58

SP - 224

EP - 231

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -

ID: 22338498