Which objects allow for a wait free implementation of (binary) consensus? The answer depends on the number of participants

The **consensus number** of an object of type T is the greatest number n such that it is possible to wait free implement a consensus object in a system of n processes by only using objects of type T and atomic R/W registers.

For all T, CN(T) > 0; if there is no sup, we let CN(T) := +∞

**Thm:** let CN(T1) < CN(T2), then there exists no wait free implementation of T2 that only uses objects of type T1 and atomic R/W registers for all n s.t. CN(T1) < n <= CN(T2).