 This idea of admitting arbitrary subsets had been one of the deep inspirations of both Cantor and Dedekind, but none of them had thematized it. (Here, their modern understanding of analysis played a crucial but implicit background role, since they worked within the Dirichlet-Riemann tradition of “arbitrary” functions.) As for the now famous iterative conception there were some elements of it (particularly in Dedekind’s work, with his iterative development of the number system, and his views on “systems” and “things”), but it was conspicuously absent from many of the relevant authors. Typically, e. g., Cantor did not iterate the process of set formation: he tended to consider sets of homogeneous elements, elements which were taken to belong “in some conceptual sphere” (either numbers, or points, or functions, or even physical particles—but not intermingled). The iterative conception was first suggested by Kurt Gödel in [1933], in connection with technical work by von Neumann and Zermelo a few years earlier; Gödel would insist on the idea in his well-known paper on Cantor’s continuum problem. It came only post facto, after very substantial amounts of set theory had been developed and fully systematized.