The theory of vector lattices, stemming from the mid-thirties, is
now at the stage where its main achievements are being summarized.
The sweeping changes of the last two decades have changed its image
completely. The range of its application was expanded and enriched
so as to embrace diverse branches of the theory of functions,
geometry of Banach spaces, operator theory, convex analysis, etc.
Furthermore, the theory of vector lattices was impregnated with
principally new tools and techniques from other sections of
mathematics. These circumstances gave rise to a series of mono
graphs treating separate aspects of the theory and oriented to
specialists. At the same time, the necessity of a book intended for
a wider readership, reflecting the modern diretions of research
became clear. The present book is meant to be an attempt at
implementing this task. Although oriented to readers making their
first acquaintance with vector-lattice theory, it is composed so
that the main topics dealt with in the book reach the current level
of research in the field, which is of interest and import for
specialists. The monograph was conceived so as to be divisible into
two parts that can be read independently of one another. The first
part is mainly Chapter 1, devoted to the so-called Boolean-valued
analysis of vector lattices. The term designates the applica tion
of the theory of Boolean-valued models by D. Scott, R. Solovay and
P.
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