 In general, for each algebra \(\mathcal{F}\) and equivalence relation \(\sim\), there is an infinite sequence   \[(\mathcal{F}, \sim) = (\mathcal{F}_0, \sim_0), (\mathcal{F}_1, \sim_1), (\mathcal{F}_2, \sim_2), \ldots\]   of pairs of algebras \(\mathcal{F}_i\) and equivalence relations \(\sim_i\) such that each \(\mathcal{F}_{i+1}\) is an extension of \(\mathcal{F}_i\) and each \(\sim_{i+1}\) is an extension of \(\sim_i\) and, for each \(i\), \(C(\sim_i)\). Using this, we can define the notion of limiting relative frequency and the associated notion of hypothetical calibration in full generality. Suppose \(\sim\) is an equivalence relation on \(\mathcal{F}\) and \(w\) is a possible world. And suppose  \[(\mathcal{F}_0, \sim_0), (\mathcal{F}_1, \sim_1), (\mathcal{F}_2, \sim_2), \ldots\]   is the sequence just mentioned. Then: