 In the second half of the nineteenth century Dedekind proved that the basic axioms of arithmetic have, up to isomorphism, exactly one model, and that the same holds for the basic axioms of Real Analysis. If a theory has, up to isomorphism, exactly one model, then it is said to be categorical. So modulo isomorphisms, arithmetic and analysis each have exactly one intended model. Half a century later Zermelo proved that the principles of set theory are “almost” categorical or quasi-categorical: for any two models \(M_1\) and \(M_2\) of the principles of set theory, either \(M_1\) is isomorphic to \(M_2\), or \(M_1\) is isomorphic to a strongly inaccessible rank of \(M_2\), or \(M_2\) is isomorphic to a strongly inaccessible rank of \(M_1\) (Zermelo 1930). In recent years, attempts have been made to develop arguments to the effect that Zermelo’s conclusion can be strengthened to a full categoricity assertion (McGee 1997; Martin 2001), but we will not discuss these arguments here.