Book:Angelo Margaris/First Order Mathematical Logic

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Angelo Margaris: First Order Mathematical Logic

Published $1967$, Dover Publications, Inc.

ISBN 0-486-66269-1.


Subject Matter


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