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[en] Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations.