Logic and Structure

by Van Dalen, Dirk; Dalen, D. Van

• ISBN13: 9783540208792
• ISBN10: 3540208798
• Edition: 4th
• Format: Paperback
• Copyright: 2004-04-28
• Publisher: Springer Verlag

Summary

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

Author Biography

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.

Table of Contents

0 Introduction	1	(4)
1 Propositional Logic	5	(52)
1.1 Propositions and Connectives	5	(10)
1.2 Semantics	15	(6)
1.3 Some Properties of Propositional logic	21	(9)
1.4 Natural Deduction	30	(10)
1.5 Completeness	40	(9)
1.6 The Missing Connectives	49	(8)
2 Predicate Logic	57	(46)
2.1 Quantifiers	57	(1)
2.2 Structures	58	(2)
2.3 The Language of a Similarity Type	60	(8)
2.4 Semantics	68	(5)
2.5 Simple Properties of Predicate Logic	73	(8)
2.6 Identity	81	(2)
2.7 Examples	83	(8)
2.8 Natural Deduction	91	(5)
2.9 Adding the Existential Quantifier	96	(3)
2.10 Natural Deduction and Identity	99	(4)
3 Completeness and Applications	103	(40)
3.1 The Completeness Theorem	103	(8)
3.2 Compactness and Skolem-Löwenheim	111	(7)
3.3 Some Model Theory	118	(17)
3.4 Skolem Functions or How to Enrich Your Language	135	(8)
4 Second Order Logic	143	(44)
5 Intuitionistic Logic	153	(1)
5.1 Constructive Reasoning	153	(3)
5.2 Intuitionistic Propositional and Predicate Logic	156	(6)
5.3 Kripke Semantics	162	(11)
5.4 Some Model Theory	173	(14)
6 Normalisation	187	(22)
6.1 Cuts	187	(5)
6.2 Normalization for Classical Logic	192	(6)
6.3 Normalization for Intuitionistic Logic	198	(11)
7 Godel's theorem	209	(48)
7.1 Primitive recursive functions	209	(9)
7.2 Partial Recursive Functions	218	(12)
7.3 Recursively enumerable sets	230	(6)
7.4 Some arithmetic	236	(6)
7.5 Representability	242	(4)
7.6 Derivability	246	(5)
7.7 Incompleteness	251	(6)
Bibliography	257	(2)
Index	259