definable. The overspill lemma, first proved by Abraham Robinson, formalizes this fact. See also Foundations of mathematics Frege's theorem Goodstein's theorem Neo-logicism Non-standard model of arithmetic Paris–Harrington theorem Presburger arithmetic Robinson arithmetic Second-order arithmetic Typographical Number Theory Notes References Citations Sources Two English translations: Derives the Peano axioms (called S) from several axiomatic set theories and from category theory. Derives the Peano axioms from ZFC Contains translations of the following two papers, with valuable commentary: Further reading External links Includes a discussion of Poincaré's critique of the Peano's axioms. Commentary on Dedekind's work. 1889 introductions Mathematical axioms Formal theories of arithmetic Logic in computer science Mathematical logic hu:Giuseppe Peano#A természetes számok Peano-axiómái