Book:Dirk van Dalen/Logic and Structure/Fourth Edition

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Dirk van Dalen: Logic and Structure (4th Edition)

Published $\text {2004}$, Springer

ISBN 978-3540208792.


This book is part of the Universitext series.


Subject Matter

  • Mathematical Logic
  • Intuitionistic Logic


Contents

0 Introduction
1 Propositional Logic
1.1 Propositions and Connectives
1.2 Semantics
1.3 Some Properties of Propositional Logic
1.4 Natural Deduction
1.5 Completeness
1.6 The Missing Connectives
2 Predicate Logic
2.1 Quantifiers
2.2 Structures
2.3 The Language of a Similarity Type
2.4 Semantics
2.5 Simple Properties of Predicate Logic
2.6 Identity
2.7 Examples
2.8 Natural Deduction
2.9 Adding the Existential Quantifier
2.10 Natural Deduction and Identity
3 Completeness and Applications
3.1 The Completeness Theorem
3.2 Compactness and Skolem-Löwenheim
3.3 Some Model Theory
3.4 Skolem Functions or How to Enrich Your Language
4 Second Order Logic
5 Intuitionistic Logic
5.1 Constructive Reasoning
5.2 Intuitionistic Propositional and Predicate Logic
5.3 Kripke Semantics
5.4 Some Model Theory
6 Normalisation
6.1 Cuts
6.2 Normalization for Classical Logic
6.3 Normalization for Intuitionistic Logic
7 Gödel's theorem
7.1 Primitive recursive functions
7.2 Partial Recursive Functions
7.3 Recursively enumerable sets
7.4 Some arithmetic
7.5 Representability
7.6 Derivability
7.7 Incompleteness
Bibliography
Index


N.B.: The inconsistent capitalization is verbatim.