Dirk van Dalen's popular textbook, 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. Includes a new section on ultra-products.

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: 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 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.

The last chapter on Gödel'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.

Features a self-contained introduction into classical and intuitionistic logic using Gentzen's natural deduction Includes the basics of recursion, proof and model theory (including a new section on ultraproducts) Gives a comprehensive account of Goedel's Incompleteness Theorem within the framework of natural deduction Includes supplementary material: sn.pub/extras

Autorentext
Dirk van Dalen studied at the University of Amsterdam, where he obtained his PhD. He has taught since 1960 at Utrecht University, where he is full professor. He also taught at MIT and Oxford. His technical work is mostly in the area of intuitionistic mathematics and logic. He uses to call attention to the benefits and challenges of constructive methods.

Klappentext

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: 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 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.

The last chapter on Gödel'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.

Zusammenfassung
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. The discussion of classical logic is concluded with a concise exposition of second-order logic.

Inhalt

Introduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normalization.- Gödel's theorem.