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Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. / Bazhenov, N. A.; Zubkov, M. V.; Marchuk, M. I.

In: Algebra and Logic, Vol. 64, No. 6, 01.2026, p. 397-401.

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

Harvard

Bazhenov, NA, Zubkov, MV & Marchuk, MI 2026, 'Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega', Algebra and Logic, vol. 64, no. 6, pp. 397-401. https://doi.org/10.1007/s10469-026-09842-4

APA

Bazhenov, N. A., Zubkov, M. V., & Marchuk, M. I. (2026). Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. Algebra and Logic, 64(6), 397-401. https://doi.org/10.1007/s10469-026-09842-4

Vancouver

Bazhenov NA, Zubkov MV, Marchuk MI. Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. Algebra and Logic. 2026 Jan;64(6):397-401. doi: 10.1007/s10469-026-09842-4

Author

Bazhenov, N. A. ; Zubkov, M. V. ; Marchuk, M. I. / Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. In: Algebra and Logic. 2026 ; Vol. 64, No. 6. pp. 397-401.

BibTeX

@article{dd145698607a4863b36f48fbc54a7703,
title = "Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega",
abstract = "A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal ωn is an m-complete Σ2n+20-set. The index set of decidably categorical structures which are elementarily equivalent to ωn, enriched by the successor relation, is an m-complete Σ2n+10-set.",
keywords = "разрешимая структура, разрешимая категоричность, индексное множество, ординал, конечно аксиоматизируемый класс, decidable structure, decidable categoricity, index set, computable ordinal, finitely axiomatizable class",
author = "Bazhenov, {N. A.} and Zubkov, {M. V.} and Marchuk, {M. I.}",
note = "Bazhenov, N.A., Zubkov, M.V. & Marchuk, M.I. Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. Algebra Logic 64, 397–401 (2026). https://doi.org/10.1007/s10469-026-09842-4 The work of N.A. Bazhenov and M. I. Marchuk is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2025-349 with the Ministry of Science and Higher Education of the Russian Federation. The work of M. V. Zubkov is supported by the Russian Science Foundation (project No. 25-21-00228).",
year = "2026",
month = jan,
doi = "10.1007/s10469-026-09842-4",
language = "English",
volume = "64",
pages = "397--401",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega

AU - Bazhenov, N. A.

AU - Zubkov, M. V.

AU - Marchuk, M. I.

N1 - Bazhenov, N.A., Zubkov, M.V. & Marchuk, M.I. Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega. Algebra Logic 64, 397–401 (2026). https://doi.org/10.1007/s10469-026-09842-4 The work of N.A. Bazhenov and M. I. Marchuk is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2025-349 with the Ministry of Science and Higher Education of the Russian Federation. The work of M. V. Zubkov is supported by the Russian Science Foundation (project No. 25-21-00228).

PY - 2026/1

Y1 - 2026/1

N2 - A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal ωn is an m-complete Σ2n+20-set. The index set of decidably categorical structures which are elementarily equivalent to ωn, enriched by the successor relation, is an m-complete Σ2n+10-set.

AB - A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal ωn is an m-complete Σ2n+20-set. The index set of decidably categorical structures which are elementarily equivalent to ωn, enriched by the successor relation, is an m-complete Σ2n+10-set.

KW - разрешимая структура

KW - разрешимая категоричность

KW - индексное множество

KW - ординал

KW - конечно аксиоматизируемый класс

KW - decidable structure

KW - decidable categoricity

KW - index set

KW - computable ordinal

KW - finitely axiomatizable class

UR - https://www.mendeley.com/catalogue/6d8c6dff-659e-35a9-b4aa-d847848a264b/

UR - https://www.scopus.com/pages/publications/105048653262

U2 - 10.1007/s10469-026-09842-4

DO - 10.1007/s10469-026-09842-4

M3 - Article

VL - 64

SP - 397

EP - 401

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 82913719