First Order Mathematical Logic

Description

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. ". . . an excellent text." — Mathematical Reviews. Exercises. Bibliography. Cover Front Page Copyright Page Preface to Dover Edition Preface to First Edition Contents 1 INTRODUCTION 1 Rules of Inference 2 Set Theory 3 Axiomatic Theories 4 Predicates and Quantifiers 5 Statement Connectives 6 The Interpretation of Predicates and Quantifiers 7 The Predicate Calculus and First Order Theories 8 The Omission of Parentheses 9 Substitution of a Term for a Variable 10 Removing and Inserting Quantifiers 11 Denials 2 THE PREDICATE CALCULUS 12 Formulation 13 The Statement Calculus 14 The Deduction Theorem 15 The Completeness Theorenl for the Statement Calculus 16 Applications of the Completeness Theorem for the Statement Calculus 17 Quantifiers 18 Equivalence and Replacement 19 Theorem Schemes 20 Normal Forms 21 Equality 3 FIRST ORDER THEORIES 22 Definition and Examples 23 Deduction 24 Number Theory 25 Consistency and Completeness 26 Truth 27 The Completeness Theorem 28 Independence 29 Completeness and Categoricity 30 Decidability 31 Godels Theorem Notes References Addendum Index of Symbols Subject Index