Logic and Structure

1. Front Matter

   Pages I-X

   PDF

2. Introduction

   • Dirk van Dalen

   Pages 1-3

3. Propositional Logic

   • Dirk van Dalen

   Pages 5-55

4. Predicate Logic

   • Dirk van Dalen

   Pages 57-103

5. Completeness and Applications

   • Dirk van Dalen

   Pages 105-145

6. Second Order Logic

   • Dirk van Dalen

   Pages 147-156

7. Intuitionistic Logic

   • Dirk van Dalen

   Pages 157-190

8. Normalisation

   • Dirk van Dalen

   Pages 191-212

9. Back Matter

   Pages 213-220

   PDF

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

• Goedel's theorem
• basic model theory
• first-order logic with natural deduction
• intuitionistic logic and semantics
• model theory
• normalisation of first-order logic
• predicate logic
• recursive functions
• second order logic

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)

• Mathematical Institute, Utrecht University, Utrecht, The Netherlands

  Dirk Dalen

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. His current project is a biography of L.E.J. Brouwer and the editing of Brouwer's correspondence.

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