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“This book teaches logic to mathematicians in just the way I would have wished。Beginning with the propositional calculus by means of truth-tables，i.e。the semantics，it proceeds to the syntactics in the form of Gentzens natural deduction。this fourth edition has a long final chapter addedon Godels incompleteness theorem。The chapter follows traditional lines but preserves the excellent quality of the earlier chapters。This is a delightful textbook，with plenty of examples for the reader。”

“This is the fourth edition of van Dalens classic textbook on logic in the popular Universitext -series。this book explains clearly all aspects of logic which a novice in this matter should learn by heart。Reading this book was a real delight。A lot of the fun was in the exercises

heartily recommend this excellent textbook； Current students may have little interest in formal mathematics

the problem will solve itself when they all have a copy on their personal bookshelf。”

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。”

作者简介：

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.I。Brouwet and the editing of Brouwer’s corre—spondence。　　

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 Structurest

　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-LSwenheim

　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 G6del’S theorem

　7.1 Primitive recursive flllnctions

　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

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