 Third and finally, ‘Hesperus’ is rigid because it picks out Hesperus in all worlds that contain Hesperus. In worlds not containing Hesperus, the designator fails to name anything other than Hesperus. There is more than one account of a rigid designator that conforms to that requirement (many do:  Rami 2019). On one basic account, a rigid designator designates its designatum in every possible world containing the designatum and in other possible worlds the designator fails to designate. In places, Kripke suggests that this is his idea: