 Now, we have a great deal of information about the structure theory of L(ℝ) under ADL(ℝ). Indeed, as we noted above, this axiom is “effectively complete” with regard to questions about L(ℝ). In contrast, the embedding axiom on its own is not sufficient to imply that L(Vλ+1) has a structure theory that fully parallels that of L(ℝ) under ADL(ℝ). However, the existence of an already rich parallel is evidence that the parallel extends, and we can supplement the embedding axiom by adding some key components. When one does so, something remarkable happens: the supplementary axioms become forcing fragile. This means that they have the potential to erase independence and provide non-trivial information about Vλ+1. For example, these supplementary axioms might settle CH and much more. 