Who first proved Peano Arithmetic is not finitely axiomatizable?

Solution 1:

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.

Solution 2:

Czesław Ryll-Nardzewski, The Role of the Axiom of Induction in the Elementary Arithmetic, Fundamenta Mathematicae 39 (1952).

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Who first proved Peano Arithmetic is not finitely axiomatizable?

Solution 1:

Solution 2:

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