Notes on Logic and Set Theory

✍ Scribed by P. T. Johnstone

• Publisher: Cambridge University Press
• Year: 1987
• Tongue: English
• Leaves: 124
• Series: Cambridge Mathematical Textbooks
• Category: Library

✦ Synopsis

A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 8
1 Universal algebra......Page 12
2 Propositional calculus......Page 22
3 First-order theories......Page 29
4 Recursive functions......Page 45
5 Zermelo-Fraenkel set theory......Page 64
6 Ordinals and well-orderings......Page 79
7 The axiom of choice......Page 89
8 Cardinal arithmetic......Page 99
9 Consistency and independence......Page 108
Index of definitions......Page 119
Index of names......Page 122