Logic and Structure

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.

Table of Contents

Chapter 1: Introduction

Chapter 2: Propositional Logic

Chapter 3: Predicate Logic

Chapter 4: Completeness and Applications

Chapter 5: Second-Order Logic

Chapter 6: lntuitionistic Logic

Chapter 7: Normalization

Chapter 8: Godel’s Theorem

About the Author

Dirk van Dalen is a notable figure in the field of logic and mathematics, particularly known for his work on the formal foundations of mathematics and his contributions to the philosophy of mathematical logic. One of the key topics often discussed in relation to mathematicians and logicians like van Dalen is Gödel’s Incompleteness Theorems.