Note on a Theorem of Putnam ' Smichael

In a 1981 book, H. Putnam claimed that in a pure relational language without equality, for any model of a relation that was neither empty nor full, there was another model that satisses the same rst order sentences. Ed Keenan observed that this was false for nite models since equality is a deenable predicate in such cases. This note shows that Putnam's claim is true for innnite models, although it requires a more sophisticated proof than the one outlined by Putnam.