The second consideration examines in more detail the relationships between the physical (or the material) objects studied and the mathematical framework. These are the “synthetic determination” relations (Hellman 1989, pp. 124–135). More specifically, we have to determine which relations among non-mathematical objects can be taken, in the antecedent of an applied mathematical statement, as the basis for specifying “the actual material situation” (Hellman 1989, p. 129). The modal structuralist proposal is to consider the models of a comprehensive theory T′. This theory embraces and links the vocabulary of the applied mathematical theory (T) and the synthetic vocabulary (S) in question, which intuitively fixes the actual material situation. It is assumed that T determines, up to isomorphism, a particular kind of mathematical structure (containing, for example, Z), and that T′ is an extension of T. In that case, a proposed “synthetic basis” will be adequate if the following condition holds: