 Ranking theory (Spohn 1988, 1990 and especially 2012) assigns numerical degrees of disbelief directly to possibilities in \(W\). A pointwise ranking function \(\kappa : W \rightarrow \bN\cup \{\infty \}\) assigns a natural number (or \(\infty\)) to each possible world in \(W\). These numbers represent the degree of disbelief you assign to each possibility. Equipped with a pointwise ranking function, we can generate a numbered partition of \(W\):