 As stated above, the third axiom is called finite minimitivity. Just as in probability theory, it can be strengthened to countable unions, resulting in countably minimitive ranking functions. Unlike probability theory, finite minimitivity can also be strenghtened to arbitrary unions, resulting in completely minimitive ranking functions. See Huber (2006) for conditions under which a ranking function defined on a field of propositions induces a pointwise ranking functions on the underlying set of possibilities.