What Is Mathematical Logic?

J. N. Crossley, C.J. Ash, C.J. Brickhill, J.C. Stillwell

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486264042
• eBook ISBN: 9780486151526
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.
The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams began to converge in the seventeenth century with the invention of the calculus, which ultimately brought mathematics and logic together. The authors then briefly indicate how such relatively modern concepts as set theory, Gödel's incompleteness theorems, the continuum hypothesis, the Löwenheim-Skolem theorem, and other ideas influenced mathematical logic.
The ideas are set forth simply and clearly in a pleasant style, and despite the book's relative brevity, there is much covered on these pages. Nonmathematicians can read the book as a general survey; students of the subject will find it a stimulating introduction. Readers will also find suggestions for further reading in this lively and exciting area of modern mathematics.

Table of contents

• Cover
• Title Page
• Copyright page
• Preface
• Contents
• Introduction
• 1. Historical Survey
• 2. The Completeness of Predicate Calculus
• 3. Model Theory
• 4. Turing Machines and Recursive Functions
• 5. Gödel’s Incompleteness Theorems
• 6. Set Theory
• Some Suggestions for Further Reading
• Index