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?
2026-03-29 02:20:48.1774750848
Who first proved Peano Arithmetic is not finitely axiomatizable?
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Czesław Ryll-Nardzewski, The Role of the Axiom of Induction in the Elementary Arithmetic, Fundamenta Mathematicae 39 (1952).