The modal structuralist then indicates that the practice of theorem proving can be regained in this framework (roughly speaking, by applying the translation scheme to each line of the original proof of the theorem under consideration). Moreover, by using the translation scheme and appropriate coding devices, one can argue that arithmetic, real analysis and, to a certain extent, even set theory are recovered in a nominalist setting (Hellman 1989, pp. 16–33, 44–47, and 53–93). In particular, ‘by making use of coding devices, virtually all the mathematics commonly encountered in current physical theories can be carried out within [real analysis]’ (Hellman 1989, pp. 45–46). However, the issue of whether set theory has been nominalized in this way is, in fact, problematic—as the modal structuralist grants. After all, it is no obvious matter to establish even the possibility of the existence of structures with inaccessibly many objects.