This brings us to the second global approach, one that promises to select the correct axiom from among V = LΩ, V = LΩS, V = LΩ(∗), and their variants. This approach is based on the remarkable analogy between the structure theory of L(ℝ) under the assumption of ADL(ℝ) and the structure theory of L(Vλ+1) under the assumption that there is an elementary embedding from L(Vλ+1) into itself with critical point below λ. This embedding assumption is the strongest large cardinal axiom that appears in the literature. 