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.
Author(s): Angelo Margaris
Year: 1990
Language: English
Pages: 222
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
