Title The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications
Book Condition New
Edition First Edition
Size 150 x 230 Mm
Publisher New Delhi, India Cambridge University Press 2007
052170877X / 9780521708777
Seller ID 020838
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis. • Lively mathematical examples and some unusual formal systems stimulate the reader from the very beginning • Suitable as an introduction to logic for students without any background in formal set theory • Supported by companion web-pages containing further material and exercises Contents Preface; How to read this book; 1. König’s lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index. Printed Pages: 216 with 4 line diagrams, 141 exercises, and 50 worked examples.