Logic and Structure (Paperback) (ISBN-13: 9781447145578)

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 Gel'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-Lenheim, 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 Gel translation, the disjunction and existence property are also included.

The last chapter on Gel'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.