 Would we get a full Boolean algebra by supplementing GEM with the Bottom axiom (P.10), i.e., by positing the mereological equivalent of the empty set? One immediate way to answer this question is in the affirmative, but only in a trivial sense: we have already seen in Section 3.4 that, under the axioms of MM, (P.10) only admits of degenerate one-element models. Such is the might of the null item. On the other hand, suppose we rely on the “non-trivial” notions of genuine parthood and genuine overlap defined in (37)–(38). And suppose we introduce a corresponding family of “non-trivial” operators for sum, product, etc. Then it can be shown that the theory obtained from GEM by adding (P.10) and replacing (P.5) and (P.153) with the following non-trivial variants: