Notes on Logic and Set Theory [Paperback]

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.Preface; 1. Universal algebra; 2. Propositional calculus; 3. First-order theories; 4. Recursive functions; 5. Zermelo - Fraenkel set theory; 6. Ordinals and well -orderings; 7. The axiom of choice; 8. Cardinal arithmetic; 9. Consistency and independence; Index of definitions; Index of names.