The Mathematics Of Logic - Kaye Richard W. | Libro Cambridge University Press 07/2007 - HOEPLI.it


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kaye richard w. - the mathematics of logic

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




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Dettagli

Genere:Libro
Lingua: Inglese
Pubblicazione: 07/2007





Sommario

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.




Prefazione

Undergraduate textbook covering the key material for a typical first course in logic, including a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. The author ensures that the number of new concepts at each stage is manageable, whilst providing lively mathematical applications throughout.




Trama

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.




Autore

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







Altre Informazioni

ISBN:

9780521882194

Condizione: Nuovo
Dimensioni: 235 x 18 x 158 mm Ø 418 gr
Formato: Copertina rigida
Illustration Notes:4 b/w illus. 141 exercises
Pagine Arabe: 206






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