  In this paper we consider a synchronous message passing system in which in
every round an external adversary is able to send each processor up to k
messages with falsified sender identities and arbitrary content. It is formally
shown that this impersonation model is slightly stronger than the asynchronous
message passing model with crash failures. In particular, we prove that
(k+1)-set agreement can be solved in this model, while k-set agreement is
impossible, for any k>=1. The different strength of the asynchronous and
impersonation models is exhibited by the order preserving renaming problem, for
which an algorithm with n+k target namespace exists in the impersonation model,
while an exponentially larger namespace is required in case of asynchrony.
