# The Mathematics of LogicA Guide to Completeness Theorems and their Applications

## £32.99

• Date Published: July 2007
• availability: Available
• format: Paperback
• isbn: 9780521708777

## £32.99 Paperback

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• 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

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## Product details

• Date Published: July 2007
• format: Paperback
• isbn: 9780521708777
• length: 216 pages
• dimensions: 225 x 153 x 10 mm
• weight: 0.304kg
• contains: 4 b/w illus. 141 exercises
• availability: Available

Preface
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.

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### The Mathematics of Logic

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• ## Author

Richard W. Kaye, University of Birmingham
Richard Kaye is a senior lecturer in pure mathematics at the University of Birmingham.

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