Boolean valued analysis is a technique for studying properties
of an arbitrary mathematical object by comparing its
representations in two different set-theoretic models whose
construction utilises principally distinct Boolean algebras. The
use of two models for studying a single object is a characteristic
of the so-called non-standard methods of analysis. Application of
Boolean valued models to problems of analysis rests ultimately on
the procedures of ascending and descending, the two natural
functors acting between a new Boolean valued universe and the von
Neumann universe.
This book demonstrates the main advantages of Boolean valued
analysis which provides the tools for transforming, for example,
function spaces to subsets of the reals, operators to functionals,
and vector-functions to numerical mappings. Boolean valued
representations of algebraic systems, Banach spaces, and involutive
algebras are examined thoroughly.
Audience: This volume is intended for classical analysts seeking
powerful new tools, and for model theorists in search of
challenging applications of nonstandard models.
General
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