Basic Set Theory

Almost all the recently-published books on set theory are of one of the following two kinds. Books of the first kind treat set theory on an elementary level which is, roughly, the level needed for studying point set topology and Steinitz's theorem on the existence of the algebraic elosure of a general field. Books of the second kind are books which give a more or less detailed exposition of several areas of set theory that are subject to intensive current research, such as constructibility, forcing, large cardinals and determinacy. Books of the first kind may serve well as an introduction to the subject but are too elementary for the student or the mathematician who wants to gain a deeper understanding of set theory. The books of the second kind usually go hurriedly through the basic parts of set theory in their justified haste to get at the more advanced topics. One of the advantages of writing a book in aseries such as the Perspectives in Mathematical Logic is that one is able to write a book on a rather advanced level covering the basic material in an unhurried pace. There is no need to reach the fron tiers of the subject as one can leave this to other books in the series. This enables the author to pay elose attention to interesting and important aspects of the subject which do not lie on the straight road to the very central topics of current research.