  We construct four-dimensional covariant non-linear theories of massive
gravity which are ghost-free in the decoupling limit to all orders. These
theories resum explicitly all the nonlinear terms of an effective field theory
of massive gravity. We show that away from the decoupling limit the Hamiltonian
constraint is maintained at least up to and including quartic order in
non-linearities, hence, excluding the possibility of the Boulware-Deser ghost
up to this order. We also show that the same remains true to all orders in a
similar toy-model.
