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Two papers on the predicate calculus / [electronic resource] by S.C. Kleene.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; no. 10.Publication details: Providence, R.I. : American Mathematical Society, 1967, c1952 (1985 printing)Edition: RevDescription: 1 online resource (68 p.)ISBN:
  • 9780821898895 (online)
Subject(s): Additional physical formats: Two papers on the predicate calculus /LOC classification:
  • QA3 .A57 no. 10
Online resources:
Contents:
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
Item type: E-BOOKS
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Includes bibliographical references.

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

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