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Logic and Structure by Dirk van Dalen

Logic and Structure

by Dirk van Dalen

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This book is exceedingly dense and very high on formalisms, and I'd say more for a grad course, or at least upper level honors undergrad. It is comprehensive and concise no doubt, but it is one of those books where the author "leaves things as an exercise to the reader" in crucial proofs. Only after having read other introductions to set theory, advanced mathematics, and logic books first would I approach this book. ( )
  divisionbyzer0 | Jun 16, 2009 |
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Amazon.com Product Description (ISBN 038712831X, Paperback)

A book which efficiently presents the basics of propositional and predicate logic, van Dalen's popular textbook contains a complete treatment classical logic on the basis of Gentzen's Natural Deduction and the traditional two-valued semantics, culminating in the completeness theorems. The first chapter, containing a leisured treatment of propostional logic, is followed by an equally elaborate chapter on predicate logic. On the basis of the material of the first of two chapters the completeness theorem is established and an excursion is made into model theory. The main facts of model theory, e.g. compactness, Skolem-Loewenheim, elementary equivalence, non-standard models, quantified elimination and Skolem functions are covered in chapter Three. The exposition of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. This chapter contains a completeness proof for Kripke's semantics and a number of specific constructive features have been incorporated, e.g. a study of equality and apartness the disjunction and existence property, the Goedel translation. A new chapter has been added at the end of this edition, with the basics of the proof theory of natural deduction; derivations are studued for their own sake and weak normalisation is proved. A choise of exercises is added ranging from simple applications of the definitions to more sophisticated problems.

(retrieved from Amazon Thu, 12 Mar 2015 18:23:36 -0400)

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