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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 3, Pages 654–668
DOI: https://doi.org/10.33048/smzh.2020.61.313 (Mi smj6008) 		 
The theories of superatomic boolean algebras with distinguished subalgebra which lack countably saturated models

D. E. Pal'chunovab, A. V. Trofimovab

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/smzh.2020.61.313
Abstract: Studying Boolean algebras with distinguished subalgebras, we establish the existence of continuum many simple superatomic Boolean algebras with distinguished subalgebra whose elementary theories are distinct and each of them lacks countably saturated models. The subalgebras coincide with the Boolean algebras modulo their Fréchet ideals.
Keywords: Boolean algebra, Boolean algebra with distinguished subalgebra, local algebra, elementary theory, finitely axiomatizable theory, solvable theory, elementary equivalence.
Received: 10.03.2020
Revised: 06.04.2020
Accepted: 08.04.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 3, Pages 516–527
DOI: https://doi.org/10.1134/S0037446620030131
Bibliographic databases:
Document Type: Article
UDC: 512.563
MSC: 35R30
Language: Russian
Citation: D. E. Pal'chunov, A. V. Trofimov, “The theories of superatomic boolean algebras with distinguished subalgebra which lack countably saturated models”, Sibirsk. Mat. Zh., 61:3 (2020), 654–668; Siberian Math. J., 61:3 (2020), 516–527
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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