  A countable group is residually finite if every nontrivial element can act
nontrivially on a finite set. When a group fails to be residually finite, we
might want to measure how drastically it fails - it could be that only finitely
many conjugacy classes of elements fail to act nontrivially on a finite set, or
it could be that the group has no nontrivial actions on finite sets whatsoever.
We define a hierarchy of properties, and construct groups which become
arbitrarily complicated in this sense.
