Table of contents

  1. Front Matter
    Pages I-X
  2. Dirk van Dalen
    Pages 1-3
  3. Dirk van Dalen
    Pages 5-52
  4. Dirk van Dalen
    Pages 53-96
  5. Dirk van Dalen
    Pages 97-144
  6. Dirk van Dalen
    Pages 145-153
  7. Dirk van Dalen
    Pages 155-185
  8. Dirk van Dalen
    Pages 187-207
  9. Dirk van Dalen
    Pages 209-255
  10. Back Matter
    Pages 257-263

About this book

Introduction

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-contained and provides a systematic exposition of the necessary recursion theory.

This new edition has been properly revised and contains a new section on ultra-products.

Keywords

Basic model theory First-order logic with natural deduction Goedel's theorem Intuitionistic logic and semantics Normalisation of first-order logic Recursive functions Second order logic

Authors and affiliations

  • Dirk van Dalen
    • 1
  1. 1.Department of PhilosophyUtrecht UniversityUtrechtNetherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4558-5
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4557-8
  • Online ISBN 978-1-4471-4558-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book