sethood

noun

1. (uncountable)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.””

   “Yiannis N. Moschovakis (2006), Notes on Set Theory, →ISBN, page 111: “Each of (II)–(VI) grants sethood to a specific, explicitly defined collection of objects, it legitimizes a special case of the most appealing (if false) General Comprehension Principle 3.3.””