The participating set problem can be solved in an asynchronous system using only registers. I will gently explain this problem and its solution, followed by a new extension, called consistent ordered partition. Next, I will present a wait-free simulation by f + 1 processes of any setconsensus algorithm that tolerates f faults. I will also describe how to extend this simulation using consistent ordered partition. Finally, I will discuss how this extension can be used to prove that, within every level m > 1 of the consensus hierarchy, there is an infinite sequence of increasingly more powerful deterministic objects.