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Two Papers on the Predicate Calculus
 
S. C. Kleene
Two Papers on the Predicate Calculus
eBook ISBN:  978-0-8218-9889-5
Product Code:  MEMO/1/10.E
List Price: $19.00
MAA Member Price: $17.10
AMS Member Price: $15.20
Add to cart
Two Papers on the Predicate Calculus
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Two Papers on the Predicate Calculus
S. C. Kleene
eBook ISBN:  978-0-8218-9889-5
Product Code:  MEMO/1/10.E
List Price: $19.00
MAA Member Price: $17.10
AMS Member Price: $15.20
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1; 1952; 68 pp
    MSC: Primary 03
  • Table of Contents
     
     
    • Chapters
    • Permutability of inferences in Gentzen’s calculi $LK$ and $LJ$
    • 1. The formal system $G$
    • 2. Relationships in a proof in $G$
    • 3. Interchange of adjacent logical inferences
    • 4. Permutability of logical inferences
    • Finite axiomatizability of theories in the predicate calculus using additional predicate symbols
    • Part I. Construction of the formal system, and proof of completeness
    • 1. $H$-numbers
    • 2. A primitive recursive enumeration of $H$-numbers
    • 3. The system $S_1$
    • 4. The systems $S_2, S_3$
    • 5. The systems $S_0,S$
    • Part II. Proof of consistency
    • 6. A non-constructive proof of consistency for the classical case
    • 7. Effect of the equality axioms with a new equality symbol
    • 8. Effect of the axioms $S_1$
    • 9. Effect of the axiom $S_2$
    • 10. Effect of the axioms of $S_3$
    • 11. Conclusion of the consistency proof
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 1; 1952; 68 pp
MSC: Primary 03
  • Chapters
  • Permutability of inferences in Gentzen’s calculi $LK$ and $LJ$
  • 1. The formal system $G$
  • 2. Relationships in a proof in $G$
  • 3. Interchange of adjacent logical inferences
  • 4. Permutability of logical inferences
  • Finite axiomatizability of theories in the predicate calculus using additional predicate symbols
  • Part I. Construction of the formal system, and proof of completeness
  • 1. $H$-numbers
  • 2. A primitive recursive enumeration of $H$-numbers
  • 3. The system $S_1$
  • 4. The systems $S_2, S_3$
  • 5. The systems $S_0,S$
  • Part II. Proof of consistency
  • 6. A non-constructive proof of consistency for the classical case
  • 7. Effect of the equality axioms with a new equality symbol
  • 8. Effect of the axioms $S_1$
  • 9. Effect of the axiom $S_2$
  • 10. Effect of the axioms of $S_3$
  • 11. Conclusion of the consistency proof
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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