In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been proved that consensus is universal in such systems, which means that this system augmented with consensus objects allows to implement any object that has a sequential specification. In this paper, we consider a more general system model called infinite arrival model where infinitely many processes may arrive and leave or crash during a run. We prove that consensus is still universal in this more general model. For that, we propose a universal construction based on a weak log that can be implementated using ...