Logic and Structure / Edition 4

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Overview

A book which efficiently presents the basics of propositional and predicate logic, van Dalen's popular textbook contains a complete treatment of elementary 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 propositional logic, is followed by an equally elaborate chapter on predicate logic. On the basis of the material of the first 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-Lowenheim, 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, in the disjunction and existence property, the Godel 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 studied for their own sake and weak normalisation is proved. A choice of exercises is added ranging from simple applications of the definitions to more sophisticated problems.
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Product Details

  • ISBN-13: 9783540208792
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/1/2008
  • Series: Universitext Series
  • Edition description: 4th ed. 2004. Corr. 2nd printing
  • Edition number: 4
  • Pages: 278
  • Product dimensions: 0.59 (w) x 9.21 (h) x 6.14 (d)

Meet the Author

Dirk van Dalen studied at the University of Amsterdam, where he obtained his PhD. He has taught since 1960 at Utrecht University, where he is full professor. He also taught at MIT and Oxford. His technical work is mostly in the area of intuitionistic mathematics and logic. He uses to call attention to the benefits and challenges of constructive methods. His current project is a biography of L.E.J. Brouwer and the editing of Brouwer's correspondence.

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Table of Contents

Introduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normalisation.- Goedel's Theorem.- Bibliography.- Index.

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