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

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.