The Mathematics of Logic
A Guide to Completeness Theorems and their Applications
Seiten
2007
Cambridge University Press (Verlag)
978-0-521-70877-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-70877-7 (ISBN)
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.
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.
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.
Richard Kaye is a senior lecturer in pure mathematics at the University of Birmingham.
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.
| Erscheint lt. Verlag | 12.7.2007 |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 4 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 225 mm |
| Gewicht | 304 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 0-521-70877-X / 052170877X |
| ISBN-13 | 978-0-521-70877-7 / 9780521708777 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
World Scientific Publishing Co Pte Ltd (Verlag)
CHF 43,60
what we have that machines don't
Buch | Softcover (2024)
Profile Books Ltd (Verlag)
CHF 19,15
how simple questions lead us to mathematics’ deepest truths
Buch | Softcover (2024)
Profile Books Ltd (Verlag)
CHF 19,15
