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Sibirskii Matematicheskii Zhurnal, 2025, Volume 66, Number 3, Pages 506–522
DOI: https://doi.org/10.33048/smzh.2025.66.313 (Mi smj7959) 		 
A superatomic Boolean algebra with a distinguished subalgebra whose theory lacks simple models

D. E. Palchunova, A. V. Trofimovb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2025.66.313
Abstract: We construct a superatomic Boolean algebra with a distinguished subalgebra whose elementary theory lacks simple models.
Keywords: Boolean algebra, Boolean algebra with a distinguished subalgebra, local algebra, elementary theory, finitely axiomatizable theory, solvable theory, elementary equivalence.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0011
The work of Palchunov was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0011).
Received: 12.09.2023
Revised: 21.02.2025
Accepted: 25.02.2025
English version:
Siberian Mathematical Journal, 2025, Volume 66, Issue 3, Pages 749–762
DOI: https://doi.org/10.1134/S0037446625030139
Document Type: Article
UDC: 512.563
MSC: 35R30
Language: Russian
Citation: D. E. Palchunov, A. V. Trofimov, “A superatomic Boolean algebra with a distinguished subalgebra whose theory lacks simple models”, Sibirsk. Mat. Zh., 66:3 (2025), 506–522; Siberian Math. J., 66:3 (2025), 749–762
Citation in format AMSBIB
\Bibitem{PalTro25}
\by D.~E.~Palchunov, A.~V.~Trofimov
\paper A~superatomic Boolean algebra with a~distinguished subalgebra whose theory lacks simple models
\jour Sibirsk. Mat. Zh.
\yr 2025
\vol 66
\issue 3
\pages 506--522
\mathnet{http://mi.mathnet.ru/smj7959}
\transl
\jour Siberian Math. J.
\yr 2025
\vol 66
\issue 3
\pages 749--762
\crossref{https://doi.org/10.1134/S0037446625030139}
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