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 G del'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 wenheim, 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 del translation, the disjunction and existence property are also included. The last chapter on G del'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.