Logic and Structure (Universitext)

Book Details

• Author: Dirk van Dalen

• Publisher: Springer

• Language: English, French

• Edition: 5th ed. 2013

• ISBN: 9781447145578

• Pages: 273

• Binding: Paperback

• Dimensions: 9.3 x 6.1 x 0.6 inches

About The Book

Dirk van Dalen’s Logic and Structure, now in its fifth edition, offers a comprehensive and accessible introduction to classical and intuitionistic logic, model theory, and Gödel's famous incompleteness theorem. Renowned for its clarity and structured approach, this book is an essential resource for students and scholars of mathematical logic and philosophy.

The book begins with an easy-to-follow presentation of propositional and predicate logic using Gentzen's natural deduction system, providing readers with a solid foundation in logical principles. It continues with a detailed exploration of model theory, including key concepts such as compactness, Skolem-Löwenheim theorem, non-standard models, and quantifier elimination.

In light of the increasing focus on constructive methods, this edition includes an in-depth discussion of intuitionistic logic and Kripke semantics. Key topics like apartness, equality, Gödel translation, and the disjunction and existence properties are also addressed in detail.

The book concludes with a self-contained chapter on Gödel's first incompleteness theorem, providing a systematic exposition of recursion theory. A new section on ultra-products has been added to this edition, further enhancing its value as a critical reference.

Logic and Structure is perfect for students of logic, mathematics, and philosophy, as well as anyone interested in the fundamental aspects of logic and its applications. Its well-organized approach and clear explanations make it an invaluable resource for learning and research.