 The extension of a predicate is invariant under a permutation of the domain if replacing each of its members with the object to which the permutation maps it leaves us with the same set we started with.  Thus, for example, the extension of “is a letter between \(\textrm{A}\) and \(\textrm{E}\)” is invariant under the permutation of letters described above. By contrast, the extension of “is a vowel between \(\textrm{A}\) and \(\textrm{E}\)”, the set \(\{\textrm{A}, \textrm{E}\}\), is not invariant under this permutation, which transforms it to a different set, \(\{\textrm{C}, \textrm{D}\}\). 