 Of course, we still need certain structural assumptions in order to prove a representation theorem for Jeffrey’s theory. In particular, the set \(\Omega\), on which the preference ordering \(\preceq\) is defined, has to be an atomless Boolean algebra of propositions, from which the impossible propositions, denoted \(\bot\), have been removed. A Boolean algebra is just a set of e.g. propositions or sentences that is closed under the classical logical operators and negation. An algebra is atomless just in case all of its elements can be partitioned into finer elements. The assumption that \(\Omega\) is atomless is thus similar to Savage’s  P6,  and can be given a similar justification: any way \(p_i\) in which \(p\) can be true can be partitioned into two further propositions according to how some coin would land if tossed.