TY - JOUR

T1 - Boolean-Valued Universe as an Algebraic System. I

T2 - Basic Principles

AU - Gutman, A. E.

N1 - Publisher Copyright: © 2019, Pleiades Publishing, Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Boolean-valued algebraic system

KW - Boolean-valued analysis

KW - set theory

UR - http://www.scopus.com/inward/record.url?scp=85073258763&partnerID=8YFLogxK

U2 - 10.1134/S0037446619050057

DO - 10.1134/S0037446619050057

M3 - Article

AN - SCOPUS:85073258763

VL - 60

SP - 810

EP - 827

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -