Logic and Structure (Universitext) - Softcover

Dalen, Dirk Van

Softcover

ISBN 10: 3540578390 ISBN 13: 9783540578390

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary

About this title

Review

From the reviews of the fourth edition: "This book teaches logic to mathematicians in just the way I would have wished. ... Beginning with the propositional calculus by means of truth-tables, i.e. the semantics, it proceeds to the syntactics in the form of Gentzen’s natural deduction. ... this fourth edition has a long final chapter added, on Gödel’s incompleteness theorem. ... The chapter follows traditional lines but preserves the excellent quality of the earlier chapters. This is a delightful textbook, with plenty of examples for the reader." (C.W. Kilmister, The Mathematical Gazette, Vol. 89(515), 2005) "This is the fourth edition of van Dalen’s classic textbook on logic in the popular ‘Universitext’ -series. ... this book explains clearly all aspects of logic which a novice in this matter should learn by heart. ... Reading this book was a real delight. A lot of the fun was in the exercises ... heartily recommend this excellent textbook; ... Current students may have little interest in formal mathematics ... the problem will solve itself when they all have a copy on their personal bookshelf." (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, Vol. 12 (3), 2005)

From the Back Cover

A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions. The discussion of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. Completeness is established for Kripke semantics. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property have been incorporated. The power and elegance of natural deduction is demonstrated best in the part of proof theory called `cut-elimination' or `normalization'. Chapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gödel's first incompleteness theorem. The chapter is self-contained, it provides a systematic exposition of primitive recursion and partial recursive functions, recursive by enumerable sets, and recursive separability. The arithmetization of Peano's arithmetic is based on the natural deduction system.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1994
• ISBN 10: 3540578390
• ISBN 13: 9783540578390
• Binding: Paperback
• Language: English
• Edition number: 3
• Number of pages: 227