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 Godel'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-Lowenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of...