Book:Angelo Margaris/First Order Mathematical Logic

Angelo Margaris: First Order Mathematical Logic

Published $\text {1967}$, Dover Publications, Inc.

ISBN 0-486-66269-1

Subject Matter

• Predicate Logic
• Mathematical Logic

Contents

• CHAPTER I. 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

• CHAPTER II. THE PREDICATE CALCULUS
  • 12. Formulation
  • 13. The Statement Calculus
  • 14. The Deduction Theorem
  • 15. The Completeness Theorem 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

• CHAPTER III. 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. Gödel's Theorem

• Notes

• References

• Indexes