author = "Gutman A.E.",

title = "Boolean-valued universe as an algebraic system. I: Basic principles",

journal = "Sib. Math. J.",

year = "2019",

volume = "60",

number = "5",

pages = "810--827",

doi = "10.1134/S0037446619050057",

annote = "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"