  One might grant that these are indeed fruitful consequences of ADL(ℝ) and as such are evidence that ADL(ℝ) holds. However, one might be concerned that perhaps there are axioms that share these fruitful consequences and yet are incompatible with ADL(ℝ). As a response, one might note that this objection is never raised in the analogous case of physics where a multitude of incompatible theories can agree in their empirical consequences. But there is a much stronger response that one can make. For in contrast to the case of physics—where one could never hope to show that there was only one theory with the desired empirical consequences—in set theory this is actually the case; more precisely, any theory that has these fruitful consequences—that is, which lifts the structure theory to the level of L(ℝ)—must imply ADL(ℝ). This remarkable fact is embodied in the following theorem: 