Introduction to Mathematical Logic, Sixth Edition

Book Preface

This book is a compact introduction to many of the important topics of mathematical logic, comprising natural and unrestricted set-theoretic methods. Here is a very brief sketch of some of its contents:

1. One of the most prominent features of this new edition is a consistency proof for formal number theory due to Kurt Schütte. This proof had been included in the first edition in 1964. It was dropped in later editions and is now brought back by “popular demand.” Quite a few people thought I had made a mistake in abandoning it.

2. There is now a greatly enlarged bibliography, with items that should be interesting to a wide audience. Many of them have to do with the philosophical significance of some important results of modern mathematical logic.

As before, the material in this book can be covered in two semesters, but Chapters 1 through 3 are quite adequate for a one-semester course. Bibliographic references are aimed at giving the best source of information, which is not always the earliest; hence, these references give no indication of priority.

I believe that the essential parts of the book can be read with ease by anyone with some experience in abstract mathematical thinking. There is, however, no specific prerequisite.

This book owes an obvious debt to the standard works of Hilbert and Bernays (1934, 1939), Kleene (1952), Rosser (1953), and Church (1956). I am also grateful to many people for their help, including my editor Jessica Vakili, as well as the editors of the earlier editions.