>>7897128A Peano structure. Those are unique up to isomorphisms, so it is justified to call one the naturals.
Such a Peano structure exists, as hinted by
>>7897522, which is the appropriate construction for set theory, but in other fields this is different, e.g. you want that (or to not trigger Wilberger), so in analysis the naturals are a different set, but they still have the same properties.
