# Book:Alan G. Hamilton/Logic for Mathematicians/Second Edition

## Alan G. Hamilton: Logic for Mathematicians (2nd Edition)

Published $\text {1988}$, Cambridge University Press

ISBN 0-521-36865-0.

### Contents

Preface
1 Informal statement calculus
1.1 Statements and connectives
1.2 Truth functions and truth tables
1.3 Rules for manipulation and substitution
1.4 Normal forms
1.6 Arguments and validity
2 Formal statement calculus
2.1 The formal system $L$
2.2 The Adequacy Theorem for $L$
3 Informal predicate calculus
3.1 Predicates and quantifiers
3.2 First order languages
3.3 Interpretations
3.4 Satisfaction, truth
3.5 Skolemisation
4 Formal predicate calculus
4.1 The formal system $K_\mathcal L$
4.2 Equivalence, substitution
4.3 Prenex form
4.4 The Adequacy Theorem for $K$
4.5 Models
5 Mathematical systems
5.1 Introduction
5.2 First order systems with equality
5.3 The theory of groups
5.4 First order arithmetic
5.5 Formal set theory
5.6 Consistency and models
6 The Gödel Incompleteness Theorem
6.1 Introduction
6.2 Expressibility
6.3 Recursive functions and relations
6.4 Gödel numbers
6.5 The incompleteness proof
7 Computability, unsolvability, undecidability
7.1 Algorithms and computability
7.2 Turing machines
7.3 Word problems
7.4 Undecidability of formal systems
Appendix: Countable and uncountable sets
Hints and solutions to selected exercises
Glossary of symbols
Index

Next

## Errata

### Double Negation with Erroneous Conjunction

Chapter $1$: Informal statement calculus: $1.2$. Truth functions and truth tables: Example $1.6 \ \text{(c)}$:

$\paren {p \leftrightarrow \paren {\land \paren {\sim p} } }$ is a tautology.

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