Logic and Structure
By: by Dirk Dalen
Contributors: SpringerLink (Online service)
Edition: 5th ed. 2013.
Series: Universitext
Publisher: Springer London; Imprint: Springer
Published: 2013
Place of publication: London
Language: eng
Format: [electronic resource] /
Number of pages: 263
ISBN-13: 9781447145585
Subjects: Mathematics; Symbolic and mathematical Logic; 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>
Table of contents: title: <p>Introduction; title: Propositional Logic; title: Predicate Logic; title: Completeness and Applications; title: Second Order Logic; title: Intuitionistic Logic; title: Normalization; title: Gödel's theorem.</p>.