Logic and Structure

By Dirk Dalen

Subjects: Symbolic and mathematical Logic, Mathematics, Logic, symbolic and mathematical, Mathematical Logic and Foundations

Description: <p>Dirk van Dalen’s popular textbook<i> Logic and Structure</i>, 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. </p><p>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. </p><p>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. </p><p>The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. </p><p>This new edition has been properly revised and contains a new section on ultra-products.</p>