  Semantics  receives rather short shrift in Armstrong's version of  combinatorialism — at least, semantics in the model theoretic  sense of   §1.2  — but, as it has played an important role in our discussion of  concretism and abstractionism, we note briefly how the ontology of  combinatorialism might be taken to populate a possible world  interpretation of the language of modal predicate logic.  Specifically, we can take the range of the modal operators —  understood, semantically, as quantifiers — to be all of the  combinatorial possible worlds in the sense of AW3. The domain  d(w) of each world w is the set of all simple  and complex objects that exist in w according to AE3  and the w-extension Iπ(w) of a  predicate π expressing a simple or complex universal R is  the set of all n-tuples, ⟨a1, ...,  an⟩ such that the atomic fact  [R,a1,...,an]  exists in w. 