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.
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Dedicated to Yu. G. Reshetnyak on the occasion of his 90th birthday.
Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 5, pp. 1041–1062.
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).
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Gutman, A.E. Boolean-Valued Universe as an Algebraic System. I: Basic Principles. Sib Math J 60, 810–827 (2019). https://doi.org/10.1134/S0037446619050057
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DOI: https://doi.org/10.1134/S0037446619050057