suppose that φ uses n parameters from l. suppose z...,z is the sequence of parameters that can be used with φ to define x, and w...,w does the same for y. then let x<y if and only if either z<w or (z=w and z<w) or (z=w and z=w and z<w) or etc.. this is called the reverse-lexicographic ordering; if there are multiple sequences of parameters that define one of the sets, we choose the least one under this ordering. it being understood that each parameter's possible values are ordered according to the restriction of the ordering of l to l, so this definition involves transfinite recursion on α.