Standard

Universal Boolean Algebras with Applications to Semantic Classes of Models. / Селиванов, Виктор Львович; Peretyat’kin, Mikhail.

Twenty Years of Theoretical and Practical Synergies (CiE 2024). ed. / Levy Patey. Springer Nature, 2024. p. 205–217 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14773 LNCS).

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

Harvard

Селиванов, ВЛ & Peretyat’kin, M 2024, Universal Boolean Algebras with Applications to Semantic Classes of Models. in L Patey (ed.), Twenty Years of Theoretical and Practical Synergies (CiE 2024). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14773 LNCS, Springer Nature, pp. 205–217, Twenty Years of Theoretical and Practical Synergies, Amsterdam, Netherlands, 8/07/24. https://doi.org/10.1007/978-3-031-64309-5_17

APA

Селиванов, В. Л., & Peretyat’kin, M. (2024). Universal Boolean Algebras with Applications to Semantic Classes of Models. In L. Patey (Ed.), Twenty Years of Theoretical and Practical Synergies (CiE 2024) (pp. 205–217). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14773 LNCS). Springer Nature. https://doi.org/10.1007/978-3-031-64309-5_17

Vancouver

Селиванов ВЛ, Peretyat’kin M. Universal Boolean Algebras with Applications to Semantic Classes of Models. In Patey L, editor, Twenty Years of Theoretical and Practical Synergies (CiE 2024). Springer Nature. 2024. p. 205–217. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-031-64309-5_17

Author

Селиванов, Виктор Львович ; Peretyat’kin, Mikhail. / Universal Boolean Algebras with Applications to Semantic Classes of Models. Twenty Years of Theoretical and Practical Synergies (CiE 2024). editor / Levy Patey. Springer Nature, 2024. pp. 205–217 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

BibTeX

@inproceedings{65b558e57f114831be51017e65febfcc,
title = "Universal Boolean Algebras with Applications to Semantic Classes of Models",
abstract = "We explore numbered Boolean algebras over levels Ξ of arithmetical and analytical hierarchies. We show the existence and uniqueness (up to computable isomorphism) of universal Boolean Ξ-algebras, determine the levels in which such algebras exist, and classify the universal algebras up to isomorphism. We apply these results to the semantic class of all countable saturated models having decidable ω-stable theories in a fixed finite rich signature. It turns out that the Tarski-Lindenbaum algebra of this class equipped with a G{\"o}del numbering of the sentences is a Boolean Σ11-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean Σ11-algebras. This determines uniquely the isomorphism type of this Boolean algebra.",
keywords = "Tarski-Lindenbaum algebra, Turing computability, class of a hierarchy, computable isomorphism, countable saturated model, decidable theory, numbered Boolean algebra, semantic class of models, ω-stable theory",
author = "Селиванов, {Виктор Львович} and Mikhail Peretyat{\textquoteright}kin",
note = "M. Peretyat{\textquoteright}kin, V. Selivanov. M. Peretyat{\textquoteright}kin, V. Selivanov. Universal Boolean Algebras with Applications to Semantic Classes of Models. L. Levy Patey et al. (Eds.): CiE 2024, LNCS 14773, pp. 205–217, 2024. https://doi.org/10.1007/978-3-031-64309-5_17; Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe, CiE 2024 ; Conference date: 08-07-2024 Through 12-07-2024",
year = "2024",
doi = "10.1007/978-3-031-64309-5_17",
language = "English",
isbn = "9783031643088",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Nature",
pages = "205–217",
editor = "Patey, {Levy }",
booktitle = "Twenty Years of Theoretical and Practical Synergies (CiE 2024)",
address = "Germany",
url = "https://events.illc.uva.nl/CiE/CiE2024/Main/",

}

RIS

TY - GEN

T1 - Universal Boolean Algebras with Applications to Semantic Classes of Models

AU - Селиванов, Виктор Львович

AU - Peretyat’kin, Mikhail

N1 - M. Peretyat’kin, V. Selivanov. M. Peretyat’kin, V. Selivanov. Universal Boolean Algebras with Applications to Semantic Classes of Models. L. Levy Patey et al. (Eds.): CiE 2024, LNCS 14773, pp. 205–217, 2024. https://doi.org/10.1007/978-3-031-64309-5_17

PY - 2024

Y1 - 2024

N2 - We explore numbered Boolean algebras over levels Ξ of arithmetical and analytical hierarchies. We show the existence and uniqueness (up to computable isomorphism) of universal Boolean Ξ-algebras, determine the levels in which such algebras exist, and classify the universal algebras up to isomorphism. We apply these results to the semantic class of all countable saturated models having decidable ω-stable theories in a fixed finite rich signature. It turns out that the Tarski-Lindenbaum algebra of this class equipped with a Gödel numbering of the sentences is a Boolean Σ11-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean Σ11-algebras. This determines uniquely the isomorphism type of this Boolean algebra.

AB - We explore numbered Boolean algebras over levels Ξ of arithmetical and analytical hierarchies. We show the existence and uniqueness (up to computable isomorphism) of universal Boolean Ξ-algebras, determine the levels in which such algebras exist, and classify the universal algebras up to isomorphism. We apply these results to the semantic class of all countable saturated models having decidable ω-stable theories in a fixed finite rich signature. It turns out that the Tarski-Lindenbaum algebra of this class equipped with a Gödel numbering of the sentences is a Boolean Σ11-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean Σ11-algebras. This determines uniquely the isomorphism type of this Boolean algebra.

KW - Tarski-Lindenbaum algebra

KW - Turing computability

KW - class of a hierarchy

KW - computable isomorphism

KW - countable saturated model

KW - decidable theory

KW - numbered Boolean algebra

KW - semantic class of models

KW - ω-stable theory

UR - https://www.mendeley.com/catalogue/1cf47d46-e523-367e-ae5c-7224bc286c25/

U2 - 10.1007/978-3-031-64309-5_17

DO - 10.1007/978-3-031-64309-5_17

M3 - Conference contribution

SN - 9783031643088

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 205

EP - 217

BT - Twenty Years of Theoretical and Practical Synergies (CiE 2024)

A2 - Patey, Levy

PB - Springer Nature

T2 - Twenty Years of Theoretical and Practical Synergies

Y2 - 8 July 2024 through 12 July 2024

ER -

ID: 126989505