TITLE: Who first proved Peano Arithmetic is not finitely axiomatizable?
QUESTION [12 upvotes]: By Peano Arithmetic I mean first order Peano Arithmetic.  The earliest proof that it is not finitely axiomatizable that I know of is R. Montague, Semantical Closure and Non-Finite Axiomatizability I. J. Symbolic Logic 29 (1964), no. 1, 59--60.  But was the result known by other means before that?

REPLY [12 votes]: In 1952 Czesław Ryll-Nardzewski proved that first order PA is not finitely axiomatizable. The proof uses nonstandard models. Andrzej Mostowski proved the same result (also in 1952) but without using nonstandard models.