Foundations of Mathematics

This book presents a survey of the foundations of mathematics. The emphasis is on a mathematical comparison of systems rather than on any exhaustive development of analysis within a single system. Nonetheless, for most systems considered, enough details are given for the development of arithemetic, and the method of constructing the other notions of analysis is indicated. The elements of the general theory of cardinal and ordinal numbers are also furnished in the course of this work. Different branches of mathematics are distinguished primarily by the problems they treat and the kinds of structures they study. In this book, foundational studies are regarded as a branch of mathematics. The intention is to present, in a straightforward way, the mathematical problems which give rise to foundational questions and the structures one is led to examine as a result of these questions.