The first is the general form of applied mathematical statements (Hellman 1989, pp. 118–124). These statements involve three crucial components: the structures that are used in applied mathematics, the non-mathematical objects to which the mathematical structures are applied, and a statement of application that specifies the particular relations between the mathematical structures and the non-mathematical objects. The relevant mathematical structures can be formulated in set theory. Let us call the set theory used in applied contexts Z. (This is second-order Zermelo set theory, which is finitely axiomatizable; I'll denote the conjunction of the axioms of Z by ∧Z.) The non-mathematical objects of interest in the context of application can be expressed in Z as Urelemente, that is, as objects that are not sets. We will take ‘U’ to be the statement that certain non-mathematical objects of interest are included as Urelemente in the structures of Z. Finally, ‘A’ is the statement of application, describing the particular relations between the relevant mathematical structures of Z and the non-mathematical objects described in U. The particular relations involved depend on the case in question. We can now present the general form of an applied mathematical statement (Hellman 1989, p. 119):