ABSTRACT
This chapter describes one of the more important axiomatizations of set theory, due to Zermelo. It traces the web of interconnections between logic on the one hand and set theory on the other, and discusses the nature of set theory itself. The relationship between logic and set theory is a delicate one. Indeed, the distinction between the two has not always been clear. Actually, it is possible to prove the completeness of such an axiomatization of truth-functional logic by other methods that make a much more modest, and almost invisible, use of set theory, but the bolder method gives a proof of particular elegance. If the principles of set theory are patterns rather than assertions, and are neither true nor false, then in one respect even the most elementary of its axioms, such as the axiom of pairs, are in the same position as the most sophisticated among them, such as the axioms of strong infinity.
