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The Mathematics of Logic: A Guide to Completeness Theorems and their Applications

The Mathematics of Logic: A Guide to Completeness Theorems and their Applications

Autorzy
Wydawnictwo Cambridge University Press
Data wydania 12/07/2007
Liczba stron 216
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
ISBN 9780521708777
Kategorie Logika matematyczna
181.85 PLN (z VAT)
$48.72 / €40.05 / £35.69 /
Produkt na zamówienie
Dostawa 3-4 tygodnie
Ilość
Do schowka

Opis książki

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 Koenig'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.

The Mathematics of Logic: A Guide to Completeness Theorems and their Applications

Spis treści

Preface; How to read this book; 1. Koenig'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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