Logic and Structure

by Dirk van Dalen

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 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-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.

Genres: Logic, Mathematics, Philosophy, Science, Reference, Nonfiction

273 pages, Paperback

First published February 1, 1980

Reviews

[Ray Schram · Rating 4 out of 5]

Not a terribly exciting introduction, but perfectly clear and good notation.

[Erdosam · Rating 4 out of 5]

This book has opened my eyes to see maths in another point of view, and find that maths is hard unless i see it in symbols.