The aim of this paper is to argue against the view that Cantor's is an iterative conception of set. I shall distinguish between the theory found in Grundlagen and Beiträge, which I call the "first theory," and that expounded in Cantor's correspondence with Dedekind and with Jourdain. I consider that Cantor's first theory encloses a naive and unrestricted concept of set, and that the set-theoretical paradoxes do therefore follow from it. In this sense, I do not support the idea that Cantorian set theory is an iterative conception of set, as maintained by Boolos, Parsons and Vang, among others, or Hallett's interpretation, which considers it from the outset as a theory of limitation of size.

Multisets (sets with repeated elements) are of interest in mathematics, physics, philosophy, logic, linguistics and computer science. The development of multiset theory is surveyed from its earliest beginnings to its most recent applications in mathematics, logic and computational mathematics.