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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 5, Pages 1041–1062
DOI: https://doi.org/10.33048/smzh.2019.60.505 (Mi smj3132) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Boolean-valued universe as an algebraic system. I: Basic principles

A. E. Gutmanab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (506 kB) Citations (2)
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DOI: https://doi.org/10.33048/smzh.2019.60.505
Abstract: The paper is devoted to the study of Boolean-valued algebraic systems of set-theoretic signature. The technique of partial elements of these systems is developed. Some formal apparatus is presented for using partial elements and Boolean-valued classes in the truth values of formulas. The predicative Boolean-valued classes are studied that admit quantification. Logical interrelations are described between the basic properties of Boolean-valued systems: the transfer, mixing, and maximum principles.
Keywords: Boolean-valued algebraic system, set theory, Boolean-valued analysis.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.2 (проект № 0314-2016-0005)
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.2, Project 0314-2019-0005).
Received: 20.07.2019
Revised: 20.07.2019
Accepted: 24.07.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 5, Pages 810–827
DOI: https://doi.org/10.1134/S0037446619050057
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. E. Gutman, “Boolean-valued universe as an algebraic system. I: Basic principles”, Sibirsk. Mat. Zh., 60:5 (2019), 1041–1062; Siberian Math. J., 60:5 (2019), 810–827
Citation in format AMSBIB
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    This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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