Grothendieck universe

A kind of universal set whose elements follow the rules of Zermelo–Fraenkel set theory, and for which, with respect to an arbitrary set, an instance of its kind which has that set as a member may be posited to exist through an additional Tarski–Grothendieck axiom (which is not part of ZF but augments it, yielding Tarski–Grothendieck set theory).