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.