Increasing interest in set theory, particularly the possibility of a set of all sets ("universal set"), has been stimulated by its relevance to computer science. This new edition, drawing heavily on Quine's theories as introduced in New Foundations, provides an accessible introduction of universal set theory to mathematicians, logicians, and philosophers. Included are expanded accounts of the set theories of Church, Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power

Philosophical considerations, which are often ignored or treated casually, are given careful consideration in this introduction. Thomas Forster places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in an original analysis of well established topics. The presentation illustrates difficult points and includes many exercises. Little previous knowledge of logic is required and only a knowledge of standard undergraduate mathematics is assumed.