Logic for Mathematicians

ISBN-10: 0521368650
ISBN-13: 9780521368650
Edition: 2nd 1988 (Revised)
Authors: A. G. Hamilton
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Description: 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  More...

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Book details

List price: $94.99
Edition: 2nd
Copyright year: 1988
Publisher: Cambridge University Press
Publication date: 9/29/1988
Binding: Paperback
Pages: 240
Size: 6.25" wide x 9.00" long x 0.75" tall
Weight: 0.748
Language: English

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.

Preface
Informal statement calculus
Statements and connectives
Truth functions and truth tables
Rules for manipulation and substitution
Normal forms
Adequate sets of connectives
Arguments and validity
Formal statement calculus
The formal system L
The Adequacy Theorem for L
Informal predicate calculus
Predicates and quantifiers
First order languages
Interpretations
Satisfaction, truth
Skolemisation
Formal predicate calculus
The formal system K[subscript se]
Equivalence, substitution
Prenex form
The Adequacy Theorem for K
Models
Mathematical systems
Introduction
First order systems with equality
The theory of groups
First order arithmetic
Formal set theory
Consistency and models
The Godel Incompleteness Theorem
Introduction
Expressibility
Recursive functions and relations
Godel numbers
The incompleteness proof
Computability, unsolvability, undecidability
Algorithms and computability
Turing machines
Word problems
Undecidability of formal systems
Countable and uncountable sets
Hints and solutions to selected exercises
References and further reading
Glossary of symbols
Index

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