Defining Fairness

We propose a definition for the class of all fairness properties of a given system. We provide independent characterizations in terms of topology, language theory and game theory. All popular notions of fairness from the literature satisfy our definition. Moreover our class is closed under union and countable intersection, and it is, in a sense, the maximal class having this property. On the way, we characterize a class of liveness properties, called constructive liveness, which is interesting by itself because it is also closed under union and countable intersection. Furthermore, we characterize some subclasses of liveness and fairness that are closed under arbitrary intersection.