The book treats Boolean valued analysis. This term signifies the technique of
studying properties of an arbitrary mathematical object by means of comparison
between its representations in two different set-theoretic models whose construction
utilizes principally distinct Boolean algebras. As these models, we usually take the
classical Cantorian paradise in the shape of the von Neumann universe and a specially-
trimmed Boolean valued universe in which the conventional set-theoretic concepts and
propositions acquire bizarre interpretations. Exposition focuses on the fundamental
properties of order bounded operators in vector lattices. This volume is intended for
the classical analyst seeking new powerful tools and for the model theorist in search
of challenging applications of nonstandard models of set theory.