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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 3, Pages 539–571
DOI: https://doi.org/10.33048/smzh.2020.61.305 (Mi smj6000) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Boolean-valued universe as an algebraic system. ii: intensional hierarchies

A. E. Gutmanab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (622 kB) Citations (1)
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DOI: https://doi.org/10.33048/smzh.2020.61.305
Abstract: Under study are the notions of transitivity, regularity, and $\sigma$-regularity for Boolean-valued algebraic systems of set-theoretic signature. The notion of a universe over an arbitrary extensional Boolean-valued system is introduced. Some description is proposed for the structure of the universe by means of various hierarchies. The results are used for proving the uniqueness of a Boolean-valued universe up to a unique isomorphism.
Keywords: Boolean-valued algebraic system, set theory, Boolean-valued analysis, universe, cumulative hierarchy.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.2 (проект № 0314-2019-0005)
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314-2019-0005).
Received: 09.03.2020
Revised: 09.03.2020
Accepted: 08.04.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 3, Pages 426–452
DOI: https://doi.org/10.1134/S0037446620030052
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. E. Gutman, “Boolean-valued universe as an algebraic system. ii: intensional hierarchies”, Sibirsk. Mat. Zh., 61:3 (2020), 539–571; Siberian Math. J., 61:3 (2020), 426–452
Citation in format AMSBIB
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    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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