The present volume continues and completes Cylindric Algebra», Part I. Substantial portions of this volume, including much of the opening chapter, can be read
independently of its predecessor, and large portions of Part I are unnecessary for
following the present material. For this reason we present here a brief, independent
introduction to this book.
The concept of cylindric algebras was created to permit the use of algebraic
methods in treating two related parts of mathematics. One of these is a very general
kind of geometry associated with basic set—theoretic notions, and the other is the
theory of deductive systems of mathematical logic. The two domains are connected
because models of deductive systems give rise in a natural way to structures within
the set—theoretical "spaces". The notion of a cylindric algebra can be considered as
a common, algebraic abstraction from its two sources.