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, including 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 are carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, and the disjunction and existence property are also included.