  A hereditary property of quivers is a property preserved by restriction to
any full subquiver. Similarly, a mutation-invariant property of quivers is a
property preserved by mutation. Using forks, a class of quivers developed by M.
Warkentin, we introduce a new hereditary and mutation-invariant property. We
prove that a quiver being mutation-equivalent to a finite number of non-forks
-- defined as having a finite forkless part -- is this new property, using only
elementary methods. Additionally, we show that a more general property --
having a finite pre-forkless part -- is also a new hereditary and
mutation-invariant property in much the same manner.
