Equivalent conditional probability systems

By defining conditional probabilities as primitives, Rényi (Acta Mathematica Academiae Scientiarum Hungaricae 6(3):285–335, 1955) provides a framework for understanding scenarios that challenge classical probability theory, such as conditioning on events with zero unconditional probability. The paper proposes a notion of equivalence among such conditional probability systems (CPSs) and shows its appealing properties (e.g., the existence of a canonical form). Additionally, we demonstrate an application of the equivalence concept by continuing the work started in Brandenburger et al. (Synthese 201(5):175, 2023) to show that, at some fundamental level, lexicographic probability systems (LPSs) and finitary CPSs are merely different ways of encoding the same probabilistic information.