 (See Shiver 2015.) It should be noted, however, that such advantages come at a cost. For regardless of the number of atoms one begins with, the axioms of AGEM impose a fixed relationship between that number, κ, and the overall number of things, which is going to be 2κ–1. As Simons (1987: 17) pointed out, this means that the possible cardinality of an AGEM-model is restricted. There are models with 1, 3, 7, 15, 2ℵ0, and many more cardinalities, but no models with, say, cardinality 2, 4, 6, or ℵ0. Obviously, this is not a consequence of (P.15i) alone but also of the other axioms of GEM (the unsupplemented pattern in Figure 2, left, satisfies (P.15i) for each i and has 2 elements, and can be expanded at will to get models of any finite cardinality, or indefinitely to get a model with ℵ0 elements, as in Figure 2, center; see also Figure 8 for a supplemented non-filtrated model of (P.151) with 4 elements and Figure 7, right, for a supplemented non-extensional model of (P.153) with 6 elements). Still, it is a fact that in the presence of such axioms each (P.15i) rules out a large number of possibilities. In particular, every finite model of AGEM—hence of GEM—is bound to involve massive violations of what Comesaña (2008) calls “primitive cardinality”, namely, the intuive thesis to the effect that, for any integer n, there could be exactly n things. And since the size of any atomistic domain can always be reached from below by taking powers, it also follows that AGEM cannot have infinite models of strongly inaccessible cardinality. Such is, as Uzquiano (2006) calls it, the “price of universality” in the context of Atomicity.