Dedekind cut
Let "r" be a ray with endpoint "a". Let the first order formulae φ and ψ define subsets "X" and "Y" of "r", such that every point in "Y" is to the right of every point of "X" (with respect to "a"). Then there exists a point "b" in "r" lying between "X" and "Y". This is essentially the Dedekind cut construction, carried out in a way that avoids quantification over sets.