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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.
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. ...