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© 2013

Logic and Structure

Textbook

Part of the Universitext book series (UTX)

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

  1. 1.Department of PhilosophyUtrecht UniversityUtrechtNetherlands

Bibliographic information

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)