The Mathematics of Logic
A Guide to Completeness Theorems and their Applications
(Sprache: Englisch)
This textbook rescues students from traditional, dry and uninspiring introductory courses in logic, quickly providing context using genuine mathematical applications.
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Produktinformationen zu „The Mathematics of Logic “
This textbook rescues students from traditional, dry and uninspiring introductory courses in logic, quickly providing context using genuine mathematical applications.
Klappentext zu „The Mathematics of Logic “
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.
Inhaltsverzeichnis zu „The Mathematics of Logic “
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.
Autoren-Porträt von Richard W. Kaye
Kaye, Richard W.Richard Kaye is a senior lecturer in pure mathematics at the University of Birmingham.
Bibliographische Angaben
- Autor: Richard W. Kaye
- 218 Seiten, mit Abbildungen, Maße: 15,2 x 22,9 cm, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 052170877X
- ISBN-13: 9780521708777
- Erscheinungsdatum: 24.08.2018
Sprache:
Englisch
Rezension zu „The Mathematics of Logic “
"Kaye (pure mathematics, U. of Birmingham) gives undergraduate and first-year graduates key materials for a first course in logic, including a full mathematical account of the Completeness Theorem for first-order logic. As he builds a series of systems increasing in complexity, and proving and discussing the Completeness Theorem for each, Kaye keeps unfamiliar terminology to a minimum and provides proofs of all the required set theoretical results. He covers K<:o>nig's Lemma (including two ways of looking at mathematics), posets and maximal elements (including order), formal systems (including post systems and compatibility as bonuses), deduction in posets (including proving statements about a poset), Boolean algebras, propositional logic (including a system for proof about propositions), valuations (including semantics for propositional logic), filters and ideals (including the algebraic theory of Boolean algebras), first-order logic, completeness and compactness, model theory (including countable models) and nonstandard analysis (including infinitesimal numbers)." --Book News
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