 Let us consider one such (very optimistic) scenario: The true analogue of the structure theory of L(ℝ) under ADL(ℝ) holds of the L(Vλ+1) of LΩS but not of any of its variants. Moreover, this structure theory is “effectively complete” for the theory of Vλ+1. Assuming that there is a proper class of λ where the embedding axiom holds, this gives an “effectively complete” theory of V. And, remarkably, part of that theory is that V must be LΩS. This (admittedly very optimistic) scenario would constitute a very strong case for axioms that resolve all of the undecided statements. 