## Two Papers on the Predicate Calculus, Issues 10-13 |

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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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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