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Applied Logic Series

An Introduction to Mathematical Logic and Type Theory

To Truth Through Proof

Authors: Andrews, Peter B.

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eBook $129.00
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  • ISBN 978-94-015-9934-4
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  • ISBN 978-1-4020-0763-7
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  • ISBN 978-90-481-6079-2
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About this Textbook

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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.

Table of contents (8 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-94-015-9934-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-1-4020-0763-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-90-481-6079-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Mathematical Logic and Type Theory
Book Subtitle
To Truth Through Proof
Authors
Series Title
Applied Logic Series
Series Volume
27
Copyright
2002
Publisher
Springer Netherlands
Copyright Holder
Peter B. Andrews
eBook ISBN
978-94-015-9934-4
DOI
10.1007/978-94-015-9934-4
Hardcover ISBN
978-1-4020-0763-7
Softcover ISBN
978-90-481-6079-2
Series ISSN
1386-2790
Edition Number
2
Number of Pages
XVIII, 390
Topics