 The difficulty in investigating the possibilities for the structure theory of L(Vλ+1) is that we have not had the proper lenses through which to view it. The trouble is that the model L(Vλ+1) contains a large piece of the universe—namely, L(Vλ+1)—and the theory of this structure is radically underdetermined. The results discussed above provide us with the proper lenses. For one can examine the structure theory of L(Vλ+1) in the context of ultimate inner models like LΩ, LΩS, LΩ(∗), and their variants. The point is that these models can accommodate the embedding axiom and, within each, one will be able to compute the structure theory of L(Vλ+1). 