 One can get even stronger composition principles by considering infinitary bounds and sums. For example, (P.11ξ) can be generalized to a principle to the effect that any non-empty set of (two or more) entities satisfying a suitable condition ψ has an upper bound. Strictly speaking, there is a difficulty in expressing such a principle in a standard first-order language. Some early theories, such as those of Tarski (1929) and Leonard and Goodman (1940), require explicit quantification over sets (see Niebergall 2009a, 2009b; Goodman produced a set-free version of the calculus of individuals in 1951). Others, such as Lewis's (1991), resort to the machinery of plural quantification of Boolos (1984). One can, however, avoid all this and achieve a sufficient degree of generality by relying on an axiom schema where sets are identified by predicates or open formulas. Since an ordinary first-order language has a denumerable supply of open formulas, at most denumerably many sets (in any given domain) can be specified in this way. But for most purposes this limitation is negligible, as normally we are only interested in those sets of objects that we are able to specify. Thus, for most purposes the following axiom schema will do, where ‘φ’ is any formula in the language and ‘ψ’ expresses the condition in question: