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Two Papers on the Predicate Calculus
eBook ISBN:  9780821898895 
Product Code:  MEMO/1/10.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 
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Two Papers on the Predicate Calculus
eBook ISBN:  9780821898895 
Product Code:  MEMO/1/10.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1952; 68 ppMSC: 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 nonconstructive 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


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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 nonconstructive 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
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