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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