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.