Logic for Mathematicians

By: A. G. Hamilton

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Paperback | 28 November 1988 | Edition Number 2

At a Glance

Paperback
238 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 1.37

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Intended for logicians and mathematicians, this text is based on Dr. Hamilton's lectures to third and fourth year undergraduates in mathematics at the University of Stirling. With a prerequisite of first year mathematics, the author introduces students and professional mathematicians to the techniques and principal results of mathematical logic. In presenting the subject matter without bias towards particular aspects, applications or developments, it is placed in the context of mathematics. To emphasize the level, the text progresses from informal discussion to the precise description and use of formal mathmematical and logical systems. The revision of this very successful textbook includes new sections on skolemization and the application of well-formed formulae to logic programming; numerous corrections have been made and extra exercises added.

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Preface	p. vii
Informal statement calculus
Statements and connectives	p. 1
Truth functions and truth tables	p. 4
Rules for manipulation and substitution	p. 10
Normal forms	p. 15
Adequate sets of connectives	p. 19
Arguments and validity	p. 22
Formal statement calculus
The formal system L	p. 27
The Adequacy Theorem for L	p. 37
Informal predicate calculus
Predicates and quantifiers	p. 45
First order languages	p. 49
Interpretations	p. 57
Satisfaction, truth	p. 59
Skolemisation	p. 70
Formal predicate calculus
The formal system K[subscript se]	p. 73
Equivalence, substitution	p. 80
Prenex form	p. 86
The Adequacy Theorem for K	p. 92
Models	p. 100
Mathematical systems
Introduction	p. 105
First order systems with equality	p. 106
The theory of groups	p. 112
First order arithmetic	p. 116
Formal set theory	p. 120
Consistency and models	p. 125
The Godel Incompleteness Theorem
Introduction	p. 128
Expressibility	p. 130
Recursive functions and relations	p. 137
Godel numbers	p. 146
The incompleteness proof	p. 150
Computability, unsolvability, undecidability
Algorithms and computability	p. 156
Turing machines	p. 164
Word problems	p. 183
Undecidability of formal systems	p. 189
Countable and uncountable sets	p. 199
Hints and solutions to selected exercises	p. 203
References and further reading	p. 219
Glossary of symbols	p. 220
Index	p. 224
Table of Contents provided by Syndetics. All Rights Reserved.

Logic for Mathematicians

At a Glance

Paperback

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How to return your order

Defective items

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