Logic and Structure

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Springer Science & Business Media, 2004 - Mathematics - 263 pages
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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
 

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Contents

Introduction
2
Predicate Logic
57
Completeness and Applications
103
Second Order Logic
143
Intuitionistic Logic
153
Normalisation
187
Gödels theorem
209
Bibliography
257
Copyright

Other editions - View all

Logic and Structure
Dirk van Dalen
Limited preview - 2008

Common terms and phrases

algebra apply argument arithmetic atoms axioms bound called cardinality closed complete computation connectives consider consistent constants construction contains Contradiction convenient converse Corollary course decidable defined Definition derivation effective elements elimination equivalence example Exercise exists extension fact finite first formula give given hence holds identity immediately interpretation introduce intuitionistic logic Kripke language Lemma look mathematics maximal means natural node normal notation Note notion Observe obtained occur partial recursive positive precise predicate logic prime primitive recursive Proof properties propositional logic propositions prove quantifier reader reason recursive functions relation replaced result rule second-order sentences sequence Show simple Skolem standard step structures substitution Suppose symbols Theorem theory true truth universal valuation variables write

References to this book

About the author (2004)

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.

Bibliographic information

QR code for Logic and Structure
TitleLogic and Structure
Universitext (1979)
Universitext (Berlin. Print)
Universitext - Springer-Verlag
Universitext Series
AuthorDirk Dalen
Editionillustrated, reprint
PublisherSpringer Science & Business Media, 2004
ISBN3540208798, 9783540208792
Length263 pages
Subjects › 

Mathematics / Logic
  
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