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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series, 27, Band 27) - Hardcover

Andrews, Peter B.

 
9781402007637: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series, 27, Band 27)
Hardcover
ISBN 10: 1402007639 ISBN 13: 9781402007637
Verlag: Springer, 2002

Inhaltsangabe

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This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability.

The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory.

Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises.

Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

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Verlag
Springer
Erscheinungsdatum
2002
Sprache
Englisch
ISBN 10 
1402007639
ISBN 13 
9781402007637
Einband
Gebundene Ausgabe
Auflage
2
Anzahl der Seiten
408
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