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In this paper, we discuss the question how Peano’s Arithmetic reached the place it occupies today in Mathematics. We compare Peano’s approach with Dedekind’s account of the subject. Then we highlight the role of Hilbert and Bernays in subsequent developments. Propositiones, quae logicae operationibus a caeteris deducuntur, sunt theoremata; quae vero non, axiomata vocavi. [Peano 1889, iv]

Dedekinds Sätze und Peanos Axiomata