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  • Textbook
  • © 2013

Logic and Structure

Authors:

  • Features a self-contained introduction into classical and intuitionistic logic using Gentzen’s natural deduction

  • Includes the basics of recursion, proof and model theory (including a new section on ultraproducts)

  • Gives a comprehensive account of Goedel’s Incompleteness Theorem within the framework of natural deduction

  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4471-4558-5
  • Instant PDF download
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  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Dirk van Dalen
    Pages 1-3
  3. Propositional Logic

    • Dirk van Dalen
    Pages 5-52
  4. Predicate Logic

    • Dirk van Dalen
    Pages 53-96
  5. Completeness and Applications

    • Dirk van Dalen
    Pages 97-144
  6. Second-Order Logic

    • Dirk van Dalen
    Pages 145-153
  7. Intuitionistic Logic

    • Dirk van Dalen
    Pages 155-185
  8. Normalization

    • Dirk van Dalen
    Pages 187-207
  9. Gödel’s Theorem

    • Dirk van Dalen
    Pages 209-255
  10. Back Matter

    Pages 257-263

About this book

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 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.

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.

Keywords

  • Basic model theory
  • First-order logic with natural deduction
  • Goedel's theorem
  • Intuitionistic logic and semantics
  • Normalisation of first-order logic
  • Recursive functions
  • Second order logic

Reviews

From the reviews of the fifth edition:

“This is the fifth edition of van Dalen’s respected and enduring logic textbook, first published in 1980. ... Intended as a text for an undergraduate course in logic, this text contains considerably more material than can be covered in one semester. … this is quite a good book and is certainly a very serious contender as a text for an undergraduate course, and should be carefully looked at by anybody teaching such a course.” (Mark Hunacek, MAA Reviews, June, 2013)

Authors and Affiliations

  • Department of Philosophy, Utrecht University, Utrecht, Netherlands

    Dirk Dalen

Bibliographic Information

  • Book Title: Logic and Structure

  • Authors: Dirk Dalen

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4471-4558-5

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London 2013

  • Softcover ISBN: 978-1-4471-4557-8

  • eBook ISBN: 978-1-4471-4558-5

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 5

  • Number of Pages: X, 263

  • Number of Illustrations: 27 b/w illustrations

  • Additional Information: 5th ed.

  • Topics: Mathematical Logic and Foundations

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4471-4558-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)