Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice

We prove that the number of bound states for the Hamiltonian of a system of three arbitrary particles interacting through pairwise attraction potentials on a three-dimensional lattice is finite in the cases where (1) none of the two-particle subsystems has a virtual level and (2) only one of the two-particle subsystems has a virtual level.