Ebook: Propositional and Predicate Calculus A Model of Argument

At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:

- the representation of mathematical statements by formulas in a formal language;

- the interpretation of formulas as true or false in a mathematical structure;

- logical consequence of one formula from others;

- formal proof;

- the soundness and completeness theorems connecting logical consequence and formal proof;

- the axiomatization of some mathematical theories using a formal language;

- the compactness theorem and an introduction to model theory.

This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.

Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.

Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

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At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:

- the representation of mathematical statements by formulas in a formal language;

- the interpretation of formulas as true or false in a mathematical structure;

- logical consequence of one formula from others;

- formal proof;

- the soundness and completeness theorems connecting logical consequence and formal proof;

- the axiomatization of some mathematical theories using a formal language;

- the compactness theorem and an introduction to model theory.

This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.

Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.

Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

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At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:

- the representation of mathematical statements by formulas in a formal language;

- the interpretation of formulas as true or false in a mathematical structure;

- logical consequence of one formula from others;

- formal proof;

- the soundness and completeness theorems connecting logical consequence and formal proof;

- the axiomatization of some mathematical theories using a formal language;

- the compactness theorem and an introduction to model theory.

This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.

Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.

Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

Content:
Front Matter....Pages i-vii
Introduction....Pages 1-16
Propositions and Truth Assignments....Pages 17-84
Formal Propositional Calculus....Pages 85-132
Predicates and Models....Pages 133-216
Formal Predicate Calculus....Pages 217-264
Some Uses of Compactness....Pages 265-307
Back Matter....Pages 309-315