A fundamental research theme in distributed computing is the comparison of systems in terms of their ability to solve basic problems such as consensus that cannot be solved in completely asynchronous systems. In particular, in a seminal work [14], Herlihy compares shared-memory systems in terms of the shared objects that they have: he proved that there are shared objects that are powerful enough to solve consensus among n processes, but are too weak to solve consensus among n + 1 processes; such objects are placed at level n of a wait-free hierarchy. The importance of this hierarchy comes from Herlihy's universality result: intuitively, every object at level n of this hierarchy can be used to implement any object shared by n processes in a wait-free manner. As in [14], we compare shared-memory systems with respect to their ability to solve consensus among n processes. But instead of comparing systems defined by the shared objects that they have, we compare readwrite systems defined by the process schedules that they allow. These systems capture a large set of systems, e.g., systems whose synchrony ranges from fully synchronous to completely asynchronous, several systems with failure detectors, and "obstruction-free" systems. In this paper, we consider read-write systems defined in terms of process schedules, and investigate the following natural question: For every n, is there a system of n processes that is strong enough to solve consensus among every subset of n -1 processes in the system, but not enough to solve consensus among all the n processes of the system? We show that the answer to the above question is "yes", and so these systems can be classified into hierarchy akin to Herlihy's hierarchy
