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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 3, Pages 617–628
DOI: https://doi.org/10.17377/smzh.2015.56.312 (Mi smj2664) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Autostability relative to strong constructivizations of Boolean algebras with distinguished ideals

D. E. Pal'chunova, A. V. Trofimovb, A. V. Turkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (335 kB) Citations (9)
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DOI: https://doi.org/10.17377/smzh.2015.56.312
Abstract: We study Boolean algebras with distinguished ideals ($I$-algebras). We proved that a local $I$-algebra is autostable relative to strong constructivizations if and only if it is a direct product of finitely many prime models. We describe complete formulas of elementary theories of local Boolean algebras with distinguished ideals and a finite tuple of distinguished constants. We show that countably categorical $I$-algebras, finitely axiomatizable $I$-algebras, superatomic Boolean algebras with one distinguished ideal, and Boolean algebras are autostable relative to strong constructivizations if and only if they are products of finitely many prime models.
Keywords: Boolean algebra, Boolean algebra with distinguished ideals, $I$-algebra, autostability, strong constructivizability, autostability relative to strong constructivizations, prime model.
Received: 26.04.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 3, Pages 490–498
DOI: https://doi.org/10.1134/S003744661503012X
Bibliographic databases:
Document Type: Article
UDC: 512.563
Language: Russian
Citation: D. E. Pal'chunov, A. V. Trofimov, A. V. Turko, “Autostability relative to strong constructivizations of Boolean algebras with distinguished ideals”, Sibirsk. Mat. Zh., 56:3 (2015), 617–628; Siberian Math. J., 56:3 (2015), 490–498
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
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