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Computable Stone spaces. / Bazhenov, Nikolay; Harrison-Trainor, Matthew; Melnikov, Alexander.

In: Annals of Pure and Applied Logic, Vol. 174, No. 9, 103304, 01.10.2023.

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

Harvard

Bazhenov, N, Harrison-Trainor, M & Melnikov, A 2023, 'Computable Stone spaces', Annals of Pure and Applied Logic, vol. 174, no. 9, 103304. https://doi.org/10.1016/j.apal.2023.103304

APA

Bazhenov, N., Harrison-Trainor, M., & Melnikov, A. (2023). Computable Stone spaces. Annals of Pure and Applied Logic, 174(9), [103304]. https://doi.org/10.1016/j.apal.2023.103304

Vancouver

Bazhenov N, Harrison-Trainor M, Melnikov A. Computable Stone spaces. Annals of Pure and Applied Logic. 2023 Oct 1;174(9):103304. doi: 10.1016/j.apal.2023.103304

Author

Bazhenov, Nikolay ; Harrison-Trainor, Matthew ; Melnikov, Alexander. / Computable Stone spaces. In: Annals of Pure and Applied Logic. 2023 ; Vol. 174, No. 9.

BibTeX

@article{e9cb2b4e6d6b47cba20dda81439fdd7f,
title = "Computable Stone spaces",
abstract = "We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any computably metrized space. In fact, in our proof we construct a right-c.e. metrized Stone space which is not homeomorphic to any computably metrized space. Then we introduce a new notion of effective categoricity for effectively compact spaces and prove that effectively categorical Stone spaces are exactly the duals of computably categorical Boolean algebras. Finally, we prove that, for a Stone space X, the Banach space C(X;R) has a computable presentation if, and only if, X is homeomorphic to a computably metrized space. This gives an unexpected positive partial answer to a question recently posed by McNicholl.",
author = "Nikolay Bazhenov and Matthew Harrison-Trainor and Alexander Melnikov",
note = "Melnikov and Harrison-Trainor were partially supported by Rutherford Discovery Fellowship (RDF-VUW1902), Royal Society Te Apārangi.The work of Bazhenov and Melnikov is supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.",
year = "2023",
month = oct,
day = "1",
doi = "10.1016/j.apal.2023.103304",
language = "English",
volume = "174",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier",
number = "9",

}

RIS

TY - JOUR

T1 - Computable Stone spaces

AU - Bazhenov, Nikolay

AU - Harrison-Trainor, Matthew

AU - Melnikov, Alexander

N1 - Melnikov and Harrison-Trainor were partially supported by Rutherford Discovery Fellowship (RDF-VUW1902), Royal Society Te Apārangi.The work of Bazhenov and Melnikov is supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2023/10/1

Y1 - 2023/10/1

N2 - We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any computably metrized space. In fact, in our proof we construct a right-c.e. metrized Stone space which is not homeomorphic to any computably metrized space. Then we introduce a new notion of effective categoricity for effectively compact spaces and prove that effectively categorical Stone spaces are exactly the duals of computably categorical Boolean algebras. Finally, we prove that, for a Stone space X, the Banach space C(X;R) has a computable presentation if, and only if, X is homeomorphic to a computably metrized space. This gives an unexpected positive partial answer to a question recently posed by McNicholl.

AB - We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any computably metrized space. In fact, in our proof we construct a right-c.e. metrized Stone space which is not homeomorphic to any computably metrized space. Then we introduce a new notion of effective categoricity for effectively compact spaces and prove that effectively categorical Stone spaces are exactly the duals of computably categorical Boolean algebras. Finally, we prove that, for a Stone space X, the Banach space C(X;R) has a computable presentation if, and only if, X is homeomorphic to a computably metrized space. This gives an unexpected positive partial answer to a question recently posed by McNicholl.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85163195822&origin=inward&txGid=a754f561df57eb3b8612bacca92b7e77

UR - https://www.mendeley.com/catalogue/a3551d3b-ff7c-39c0-9855-df5aa528bbb9/

U2 - 10.1016/j.apal.2023.103304

DO - 10.1016/j.apal.2023.103304

M3 - Article

VL - 174

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 9

M1 - 103304

ER -

ID: 53978703