 (See e.g. Simons 1987: 42.) These postulates are mutually incompatible, but taken in isolation they can consistently be added to any standard mereological theory X considered here. Adding (P.7) yields a corresponding Atomistic version, AX; adding (P.8) yields an Atomless version, ÃX. Since finitude together with the antisymmetry of parthood (P.3) jointly imply that mereological decomposition must eventually come to an end, it is clear that any finite model of M—and a fortiori of any extension of M—must be atomistic. Accordingly, an atomless mereology ÃX admits only models of infinite cardinality. An example of such a model, establishing the consistency of the atomless versions of most standard mereologies considered in this survey, is provided by the regular open sets of a Euclidean space, with ‘P’ interpreted as set-inclusion (Tarski 1935). On the other hand, the consistency of an atomistic theory is typically guaranteed by the trivial one-element model (with ‘P’ interpreted as identity), though one can also have models of atomistic theories that allow for infinite domains. A case in point is provided by the closed intervals on the real line, or the closed sets of a Euclidean space (Eberle 1970). In fact, it turns out that even when X is as strong as the full calculus of individuals, corresponding to the theory GEM of Section 4.4, there is no purely mereological formula that says whether there are finitely or infinitely many atoms, i.e., that is true in every finite model of AX but in no infinite model (Hodges and Lewis 1968).