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Algebra i logika, 2024, Volume 63, Number 3, Pages 271–279
DOI: https://doi.org/10.33048/alglog.2024.63.303 (Mi al2806) 		 
Isomorphism of atomless Boolean algebras with distinguished ideal

S. S. Goncharovab, J. Xiangb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.33048/alglog.2024.63.303
Abstract: An algebraic, model-theoretic, and algorithmic theory of enriched Boolean algebras with distinguished ideals was developed in a series of papers by D. E. Pal'chunov, A. Touraille, P. E. Alaev, N. T. Kogabaev, and other authors. Here we study the problem on the number of countable Boolean algebras with distinguished ideals for the case when an algebra and its quotient with respect to a distinguished ideal are atomless. It is proved that, for this subclass, there exist continuum many such countable structures.
Keywords: isomorphism problem, Boolean algebra with finitely many distinguished ideals (I-algebra), density of ideal, quotient algebra with respect to ideal.
Funding agency Grant number
Russian Science Foundation 23-11-00170
China Scholarship Council
S. S. Goncharov and J. Xiang are supported by Russian Science Foundation, project No. 23-11-00170. J. Xiang is also supported by the CSC (China).
Received: 20.10.2024
Revised: 11.04.2025
English version:
Algebra and Logic, 2024, Volume 63, Issue 3, Pages 179–185
DOI: https://doi.org/10.1007/s10469-025-09781-6
Document Type: Article
UDC: 517.1+519.5
Language: Russian
Citation: S. S. Goncharov, J. Xiang, “Isomorphism of atomless Boolean algebras with distinguished ideal”, Algebra Logika, 63:3 (2024), 271–279; Algebra and Logic, 63:3 (2024), 179–185
Citation in format AMSBIB
\Bibitem{GonXia24}
\by S.~S.~Goncharov, J.~Xiang
\paper Isomorphism of atomless Boolean algebras with distinguished ideal
\jour Algebra Logika
\yr 2024
\vol 63
\issue 3
\pages 271--279
\mathnet{http://mi.mathnet.ru/al2806}
\transl
\jour Algebra and Logic
\yr 2024
\vol 63
\issue 3
\pages 179--185
\crossref{https://doi.org/10.1007/s10469-025-09781-6}
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