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

Subject Matter

• Logic
• Mathematical Logic

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

Next

Further Editions

• 1978: Alan G. Hamilton: Logic for Mathematicians

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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