Rigid designator

In modal logic and the philosophy of language, a term is said to be a rigid designator when it designates (picks out, denotes, refers to) the same thing in all possible worlds in which that thing exists and does not designate anything else in those possible worlds in which that thing does not exist. A designator is persistently rigid if it designates the same thing in every possible world in which that thing exists and designates nothing in all other possible worlds. A designator is obstinately rigid if it designates the same thing in every possible world, period, whether or not that thing exists in that world. Rigid designators are contrasted with non-rigid or flaccid designators, which may designate different things in different possible worlds.