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We study the Hamiltonian structure of tri-gravity and four-gravity in theframework of ADM decomposition of the corresponding metrics. Hence we candeduce the general structure of the constraint system of multi-gravity. We willshow it is possible and consistent to assume additional constraints whichprovide the needed first class constraints for generating diffeomorphism aswell as enough second class constraints to omit the ghosts.

Hamiltonian formalism of the ghost free Tri(-Multi)gravity theory