Although Mereology cannot by itself manage to formalize most of ordinary mathematics, yet still it is not too far from it! An addition of a single primitive with rather trivial axioms about it can result in a system strong enough to interpret full second order arithmetic and thus most of ordinary mathematics! For example add to [Atomic General Extensional Mereology (AGEM)][1] a primitive one place coding injective partial function $F$ that uniquely sends any pair of atoms (objects having no more than two atoms as parts of) to an atom, provided that there is an atom outside of the range of $F$. Now this coding function $F$ is very trivial, yet still its addition to AGEM would interpret [full second order arithmetic $Z_2$][2]. One cannot do that for example with Identity theory, we cannot top it with alike trivial primitive function to result in a theory that can interpret most of mathematics, yet still, one hears of [first order logic with equality (or identity)][3], actually one sees many expositions of axiomatic set theory as formal extensions of first order logic with identity, see for example [this][4] Wikipedia exposition of ZFC. This appears in some sense unfair to Mereology. One would have expected to see many generally known axiomatic systems topping Mereology in which a sizable amount of mathematics can be encoded. Actually as far as formalizing "ordinary mathematics" is concerned, the set concept seems to be too excessive, the standard formal capture of the set concept is ZFC which is far much stronger than a formal theory needed to capture what most people know of as mathematics, one would think that what is needed for that strength is actually *Mereology plus* theories, i.e. Mereological theories topped with some trivial mathematical concepts, like the system spoken about above, in which most of ordinary mathematics is encodable! rather than a sky-high formal system (like ZFC) far beyond what is really needed.


  [1]: https://en.wikipedia.org/wiki/Mereology
  [2]: https://en.wikipedia.org/wiki/Second-order_arithmetic
  [3]: https://en.wikipedia.org/wiki/First-order_logic#Equality_and_its_axioms
  [4]: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory