 This means that in an extensional mereology ‘O’ could be used as a primitive and ‘P’ defined accordingly, as in Goodman (1951), and it can be checked that the theory defined by postulating (61) together with the Unrestricted Sum principle (P.153) and the Antisymmetry axiom (P.3) is equivalent to GEM (Eberle 1967). Another elegant axiomatization of GEM, due to an earlier work of Tarski  (1929),[23]  is obtained by taking just the Transitivity axiom (P.2) together with the Sum2-analogue of the Unique Unrestricted Sum axiom (P.18). By contrast, it bears emphasis that the result of adding (P.153) to MM is not equivalent to GEM, contrary to the “standard” characterization given by Simons (1987: 37) and inherited by much literature that followed, including Casati and Varzi (1999) and the first edition of this  entry.[24]  This follows immediately from Pontow's (2004) counterexample mentioned at the end of Section 4.3, since the non-extensional model in Figure 4 satisfies (P.153), and was first noted in Pietruszczak (2000, n. 12). More generally, in Section 4.2 we have mentioned that in the presence of the binary Product postulate (P.13ξ), with ξ construed as overlap, the Strong Supplementation axiom (P.5) follows from the weaker Supplementation axiom (P.4). However, the model shows that the postulate is not implied by (P.153) any more than it is implied by its restricted variants (P.15ψ,3). Apart from its relevance to the proper characterization of GEM, this result is worth stressing also philosophically, for it means that (P.153) is by itself too weak to generate a sum out of any specifiable set of objects. In other words, fully unrestricted composition calls for extensionality, on pain of giving up both supplementation principles. The anti-extensionalist should therefore keep that in mind. (On the other hand, a friend of extensionality may welcome this result as an argument in favor of adopting (P.152) instead of (P.153), for we have already noted that such a way of sanctioning unrestricted composition turns out to be enough, in MM, to entail Strong Supplementation along with the existence of all products and, with them, of all sums; see Varzi 2009, with discussion in Rea 2010 and Cotnoir 2016 . In this sense, the standard way of characterizing composition given in (35), on which (P.152) is based, is not as neutral as it might seem. On this and related matters, indicating that the axiomatic path to “classical extensional mereology” is no straightforward business, see also Hovda 2009 and Gruszczyński and Pietruszczak 2014.) 