Roughly speaking, what Field established was how to extend Hilbert's results about space to space-time. Similarly to Hilbert's approach, instead of formulating Newtonian laws in terms of numerical functors, Field showed that they can be recast in terms of comparative predicates. For example, instead of adopting a functor such as ‘the gravitational potential of x’, which is taken to have a numerical value, Field employed a comparative predicate such as ‘the difference in gravitational potential between x and y is less than that between z and w’. Relying on a body of representation theorems (which plays the same role as Hilbert's representation theorem in geometry), Field established how several numerical functors can be ‘obtained’ from comparative predicates. But in order to use those theorems, he first showed how to formulate Newtonian numerical laws (such as, Poisson's equation for the gravitational field) only in terms of comparative predicates. The result (Field 1989, pp. 130–131) is the following extended representation theorem. Let N be a theory formulated only in terms of comparative predicates (with no recourse to numerical functors). For any model S of N whose domain is constituted by space-time regions, there exists: