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

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## Alan G. Hamilton:

## Contents

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

Published $1988$, **Cambridge University Press**

- ISBN 0-521-36865-0.

### Subject Matter

### 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
- 1.5 Adequate sets of connectives
- 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**

**References and further reading**

**Glossary of symbols**

**Index**

## Further Editions

## 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.