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Logic for Mathematicians - A. G. Hamilton

Logic for Mathematicians

Paperback

Published: 28th November 1988
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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.

Prefacep. vii
Informal statement calculus
Statements and connectivesp. 1
Truth functions and truth tablesp. 4
Rules for manipulation and substitutionp. 10
Normal formsp. 15
Adequate sets of connectivesp. 19
Arguments and validityp. 22
Formal statement calculus
The formal system Lp. 27
The Adequacy Theorem for Lp. 37
Informal predicate calculus
Predicates and quantifiersp. 45
First order languagesp. 49
Interpretationsp. 57
Satisfaction, truthp. 59
Skolemisationp. 70
Formal predicate calculus
The formal system K[subscript se]p. 73
Equivalence, substitutionp. 80
Prenex formp. 86
The Adequacy Theorem for Kp. 92
Modelsp. 100
Mathematical systems
Introductionp. 105
First order systems with equalityp. 106
The theory of groupsp. 112
First order arithmeticp. 116
Formal set theoryp. 120
Consistency and modelsp. 125
The Godel Incompleteness Theorem
Introductionp. 128
Expressibilityp. 130
Recursive functions and relationsp. 137
Godel numbersp. 146
The incompleteness proofp. 150
Computability, unsolvability, undecidability
Algorithms and computabilityp. 156
Turing machinesp. 164
Word problemsp. 183
Undecidability of formal systemsp. 189
Countable and uncountable setsp. 199
Hints and solutions to selected exercisesp. 203
References and further readingp. 219
Glossary of symbolsp. 220
Indexp. 224
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521368650
ISBN-10: 0521368650
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 240
Published: 28th November 1988
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.37 x 15.39  x 1.6
Weight (kg): 0.36
Edition Number: 2
Edition Type: Revised