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Two Papers on the Predicate Calculus

, Issues 10-13
Front Cover
1 Review
American Mathematical Society, 1952 - Calculus - 68 pages

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I only read the section on finite axiomitizability, but I think it includes an excellent result and the presentation is good, but not great. I am unsure why this paper isn't popular among logicians.

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Contents

Section 1
1
Section 2
26
Section 3
27

2 other sections not shown

Common terms and phrases

altered figure antecedent application axiomatic set theory CLASSICAL SYSTEM closed formula conclusion congruent consistency proof constructed containing contractions convert corresponding descendant endsequent equality axioms finitely axiomatizable formal system free variables function symbols Gentzen's given deduction given formula occurrence given proof hypothesis individual and function induction inferences belonging interchange intuitionistic system Lemma 12 Lemmas P4 logical inferences logical symbol occurrences logioal lowest inference mrof natural number non-logical axioms non-logical symbols ofrop olass P-formula belonging predicate calculus predioate preserving the pure primitive recursive function principal formula principal H-number proof in G proof or deduction property of Lemma pure variable proof pure variable property Q+3R R+3Q rank r+1 recursively enumerable relation of immediate replaced restriction on variables rules of inference sequent side formula structural inferences subformulas substitution succedent system G Theorem Pl thinning traceable two-premise inference

References to this book

From Google Scholar

Indexed systems of sequents and cut-elimination
Grigori Mints - 1997 - Journal of Philosophical Logic
A Model Based Cut Elimination Proof
Olivier Hermant
A new decidable Horn fragment of predicate calculus
V P Orevkov - 2006 - Journal of Mathematical Sciences

References from web pages

JSTOR: Papers on Predicate Calculus
Two papers on the predicate calculus, by sc Kleene (Memoirs of the American Math- ematical Society, no. 10), lithographed, Providence 1952, pp. 1-26. ...
links.jstor.org/ sici?sici=0022-4812(195403)19%3A1%3C62%3APOPC%3E2.0.CO%3B2-0

Bibliographic information

QR code for Two Papers on the Predicate Calculus
TitleTwo Papers on the Predicate Calculus, Issues 10-13
Issue 10 of American Mathematical Society. Memoirs, no.10
Volume 10 of Memoirs of the American Mathematical Society, American Mathematical Society
Issues 1-10 of Memoirs Series
AuthorStephen Cole Kleene
PublisherAmerican Mathematical Society, 1952
Length68 pages
  
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