Overview
- Features a self-contained introduction into classical and intuitionistic logic using Gentzen’s natural deduction
- Includes the basics of recursion, proof and model theory (including a new section on ultraproducts)
- Gives a comprehensive account of Goedel’s Incompleteness Theorem within the framework of natural deduction
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
Keywords
About this book
Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem.
Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic.
In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included.
The last chapter on Gödel's first incompleteness theorem is self-containedand provides a systematic exposition of the necessary recursion theory.
This new edition has been properly revised and contains a new section on ultra-products.
Reviews
From the reviews of the fifth edition:
“This is the fifth edition of van Dalen’s respected and enduring logic textbook, first published in 1980. ... Intended as a text for an undergraduate course in logic, this text contains considerably more material than can be covered in one semester. … this is quite a good book and is certainly a very serious contender as a text for an undergraduate course, and should be carefully looked at by anybody teaching such a course.” (Mark Hunacek, MAA Reviews, June, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: Logic and Structure
Authors: Dirk Dalen
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-4558-5
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2013
Softcover ISBN: 978-1-4471-4557-8Published: 13 November 2012
eBook ISBN: 978-1-4471-4558-5Published: 13 November 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 5
Number of Pages: X, 263
Number of Illustrations: 27 b/w illustrations
Additional Information: 5th ed.