Peano axioms successfully define natural numbers despite the existence of non-standard models

The claim addresses the foundational mathematical status of Peano arithmetic in relation to non-standard models. While paper [0] discusses non-standard models of arithmetic in detail, the core premise that Peano axioms successfully define natural numbers despite such models is a standard, definitional aspect of mathematical logic and model theory rather than a disputed empirical hypothesis. Therefore, the statement functions as common knowledge within mathematical logic, requiring no specific citation receipt for validation.