A non-computable c.e. closed subset of [0,1]

A non-computable c.e. closed subset of [0,1] Full article

Journal

Journal of Logic and Computation
ISSN: 0955-792X , E-ISSN: 1465-363X

Output data

Year: 2025, Volume: 35, Number: 6, Article number : exaf043, Pages count : 19 DOI: 10.1093/logcom/exaf043

Authors

Badaev Serikzhan ¹ , Bazhenov Nikolay ^2,3 , Goncharov Sergey ³ , Kalmurzayev Birzhan ¹ , Melnikov Alexander ⁴

Affiliations

1	Kazakh-British Technical University, School of Applied Mathematics , 59 Tole Bi Street, Almaty, 050000
2	Nazarbayev University , Department of Mathematics, 53 Qabanbaybatyr Avenue, Astana, 010000
3	Sobolev Institute of Mathematics , Laboratory of Computability Theory and Applied Logic, 4 Academician Koptyug Avenue, Novosibirsk, 630090
4	Victoria University of Wellington , School of Mathematics and Statistics, Kelburn Parade, Wellington, 6012

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0011

We prove that there exists a Σ01 closed subset of [0, 1] that is not homeomorphic to any computably compact space. We show that the index set of c.e. subspaces of [0, 1] that admit a computably compact presentation is not arithmetical, as witnessed by subsets of [0, 1]. The index set result is new for computable Polish spaces in general, not only for those realised as c.e. closed subsets of [0, 1]

Badaev S. , Bazhenov N. , Goncharov S. , Kalmurzayev B. , Melnikov A.
A non-computable c.e. closed subset of [0,1]
Journal of Logic and Computation. 2025. V.35. N6. exaf043 :1-19. DOI: 10.1093/logcom/exaf043 WOS Scopus OpenAlex

Submitted:	Apr 1, 2025
Published print:	Aug 12, 2025
Published online:	Aug 12, 2025

Web of science:	WOS:001548905400001
Scopus:	2-s2.0-105013110986
OpenAlex:	W4413184976

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