 As a further step, Dedekind appeals again to the notion of “creation”.  Starting with some simple infinity constructed initially—it doesn’t matter which one we start with, given their isomorphism—he “creates” new objects corresponding to its elements, thereby introducing a distinguished simple infinity Dedekind calls “the natural  numbers”.  As we saw, this last step is parallel to his introduction of “the real  numbers” (a parallel confirmed in Dedekind 1888b); but some aspects are clearer in the present case. Namely, the newly created objects are characterized completely by all arithmetic truths, i.e., by those truths transferable, or invariant, in the sense explained above. In other words, their identity depends on relational or structural properties alone, unlike for the elements of other simple infinities where intrinsic, non-arithmetic, or  “foreign” properties are built in. In passing, Dedekind also uses the name “abstraction”  for the step from the initially constructed simple infinity to the newly introduced one. (If Dedekind is interpreted along such lines, his position is a form of non-eliminative structuralism; cf. Reck 2003; but see Sieg &amp; Morris 2018 and Benis-Sinaceur 2008, 2015, 2017, respectively, for two alternative interpretations. We will again come back to this issue in Section 3.)