Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied Logic Series (APLS, volume 27)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com  for more information.
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.
Authors and Affiliations
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Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA
Peter B. Andrews
Bibliographic Information
Book Title: An Introduction to Mathematical Logic and Type Theory
Book Subtitle: To Truth Through Proof
Authors: Peter B. Andrews
Series Title: Applied Logic Series
DOI: https://doi.org/10.1007/978-94-015-9934-4
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Peter B. Andrews 2002
Hardcover ISBN: 978-1-4020-0763-7Published: 31 July 2002
Softcover ISBN: 978-90-481-6079-2Published: 09 December 2010
eBook ISBN: 978-94-015-9934-4Published: 17 April 2013
Series ISSN: 1386-2790
Edition Number: 2
Number of Pages: XVIII, 390
Topics: Mathematical Logic and Foundations, Artificial Intelligence, Logic, Artificial Intelligence, Computational Linguistics