One of the technical advances of (1991a) and (1993d) was that they showed how a structuralist account of set theory was even possible. This part of the work was co-authored with John P. Burgess and A. P. Hazen. Given a large enough universe (i.e., that the cardinality of the mereological atoms is an inaccessible cardinal), and given plural quantification, we can say exactly what constraints a function must satisfy for it to do the work we want the singleton function to do. (By ‘the singleton f