sethood

noun1

1. •
   The state of being a set.

   • William Van Ormen Quine (1969), Set Theory and Its Logic, →ISBN, page 302: “In the first edition I relativized the sethood condition insufficiently, failing to restrict the bound variables to sets”
   • John Bigelow and Robert Pargetter (1990), Science and Necessity, →ISBN, page 368: “In fact, this can be used as a necessary condition for sethood: a universal is a set only if any given thing instantiates it either in all possible worlds or in none.”