Propositional and Predicate Calculus A Model of Argument

  • DerekĀ Goldrei

Table of contents

  1. Front Matter
    Pages i-vii
  2. Pages 1-16
  3. Pages 133-216
  4. Pages 265-307
  5. Back Matter
    Pages 309-315

About this book

Introduction

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.

Keywords

Addition First-order logic Model Theory Predicate Calculus Propositional Calculus compactness theorem mathematical logic proof

Authors and affiliations

  • DerekĀ Goldrei
    • 1
  1. 1.Open UniversityMilton KeynesUK

Bibliographic information

  • DOI https://doi.org/10.1007/1-84628-229-2
  • Copyright Information Springer-Verlag London Limited 2005
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-85233-921-0
  • Online ISBN 978-1-84628-229-4
  • About this book