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On a Computability-Theoretic Approach to Boolean-Valued Models. / Bazhenov, Nikolay; Mustafa, Manat.

Lecture Notes in Computer Science. Vol. 16084 Springer Singapore, 2026. p. 79-92 7 (Lecture Notes in Computer Science; Vol. 16084 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Bazhenov, N & Mustafa, M 2026, On a Computability-Theoretic Approach to Boolean-Valued Models. in Lecture Notes in Computer Science. vol. 16084, 7, Lecture Notes in Computer Science, vol. 16084 LNCS, Springer Singapore, pp. 79-92, 19th Annual Conference, Jinan, China, 19.09.2025. https://doi.org/10.1007/978-981-95-4839-2_7

APA

Bazhenov, N., & Mustafa, M. (2026). On a Computability-Theoretic Approach to Boolean-Valued Models. In Lecture Notes in Computer Science (Vol. 16084, pp. 79-92). [7] (Lecture Notes in Computer Science; Vol. 16084 LNCS). Springer Singapore. https://doi.org/10.1007/978-981-95-4839-2_7

Vancouver

Bazhenov N, Mustafa M. On a Computability-Theoretic Approach to Boolean-Valued Models. In Lecture Notes in Computer Science. Vol. 16084. Springer Singapore. 2026. p. 79-92. 7. (Lecture Notes in Computer Science). doi: 10.1007/978-981-95-4839-2_7

Author

Bazhenov, Nikolay ; Mustafa, Manat. / On a Computability-Theoretic Approach to Boolean-Valued Models. Lecture Notes in Computer Science. Vol. 16084 Springer Singapore, 2026. pp. 79-92 (Lecture Notes in Computer Science).

BibTeX

@inproceedings{3a9ba375f54943beb7fc92942f8d3e28,
title = "On a Computability-Theoretic Approach to Boolean-Valued Models",
abstract = "The paper outlines a possible computability-theoretic approach to the theory of Boolean-valued models. We introduce the notion of a decidable Boolean-valued model А. This notion is a natural extension of the classical definition of a decidable structure. Intuitively speaking, in order to formally define А, one needs to (algorithmically) work only with countably many truth values taken from a computable Boolean algebra. This convention allows us to view such А through the lens of computable structure theory.We show that the introduced approach provides a rich class of computable structures. We prove that any possible computable dimension can be realized by an appropriately constructed, decidable Boolean-valued model А. Consequently, there exists a model А having computable dimension 2 (that is, А possesses precisely two computable presentations, up to computable isomorphisms). In contrast, it is known that dimension 2 can be realized neither by a classical decidable structure nor by a computable Boolean algebra.",
author = "Nikolay Bazhenov and Manat Mustafa",
note = "Bazhenov, N., Mustafa, M. (2026). On a Computability-Theoretic Approach to Boolean-Valued Models. In: Li, M., Xia, M., Zhang, P. (eds) Theory and Applications of Models of Computation. TAMC 2025. Lecture Notes in Computer Science, vol 16084. Springer, Singapore. https://doi.org/10.1007/978-981-95-4839-2_7 The work was supported by Nazarbayev University Faculty Development Competitive Research Grants 201223FD8823. The authors are grateful to the anonymous referees for their helpful comments.; 19th Annual Conference, TAMC 2025 ; Conference date: 19-09-2025 Through 21-09-2025",
year = "2026",
month = jan,
day = "2",
doi = "10.1007/978-981-95-4839-2_7",
language = "English",
isbn = "978-981-95-4838-5",
volume = "16084",
series = "Lecture Notes in Computer Science",
publisher = "Springer Singapore",
pages = "79--92",
booktitle = "Lecture Notes in Computer Science",
address = "Singapore",

}

RIS

TY - GEN

T1 - On a Computability-Theoretic Approach to Boolean-Valued Models

AU - Bazhenov, Nikolay

AU - Mustafa, Manat

N1 - Conference code: 19

PY - 2026/1/2

Y1 - 2026/1/2

N2 - The paper outlines a possible computability-theoretic approach to the theory of Boolean-valued models. We introduce the notion of a decidable Boolean-valued model А. This notion is a natural extension of the classical definition of a decidable structure. Intuitively speaking, in order to formally define А, one needs to (algorithmically) work only with countably many truth values taken from a computable Boolean algebra. This convention allows us to view such А through the lens of computable structure theory.We show that the introduced approach provides a rich class of computable structures. We prove that any possible computable dimension can be realized by an appropriately constructed, decidable Boolean-valued model А. Consequently, there exists a model А having computable dimension 2 (that is, А possesses precisely two computable presentations, up to computable isomorphisms). In contrast, it is known that dimension 2 can be realized neither by a classical decidable structure nor by a computable Boolean algebra.

AB - The paper outlines a possible computability-theoretic approach to the theory of Boolean-valued models. We introduce the notion of a decidable Boolean-valued model А. This notion is a natural extension of the classical definition of a decidable structure. Intuitively speaking, in order to formally define А, one needs to (algorithmically) work only with countably many truth values taken from a computable Boolean algebra. This convention allows us to view such А through the lens of computable structure theory.We show that the introduced approach provides a rich class of computable structures. We prove that any possible computable dimension can be realized by an appropriately constructed, decidable Boolean-valued model А. Consequently, there exists a model А having computable dimension 2 (that is, А possesses precisely two computable presentations, up to computable isomorphisms). In contrast, it is known that dimension 2 can be realized neither by a classical decidable structure nor by a computable Boolean algebra.

UR - https://www.scopus.com/pages/publications/105028304106

UR - https://www.mendeley.com/catalogue/f4ac9c7a-0eb6-3eb6-9b86-bdd50c776331/

U2 - 10.1007/978-981-95-4839-2_7

DO - 10.1007/978-981-95-4839-2_7

M3 - Conference contribution

SN - 978-981-95-4838-5

VL - 16084

T3 - Lecture Notes in Computer Science

SP - 79

EP - 92

BT - Lecture Notes in Computer Science

PB - Springer Singapore

T2 - 19th Annual Conference

Y2 - 19 September 2025 through 21 September 2025

ER -

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