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If M is a proper class inner model of ZFC and omega_2^M=omega_2, then everysound mouse projecting to omega and not past 0-pistol belongs to M. In fact,under the assumption that 0-pistol does not belong to M, K^M \| omega_2 isuniversal for all countable mice in V.  Similarly, if M is a proper class inner model of ZFC, delta>omega_1 isregular, (delta^+)^M = delta^+, and in V there is no proper class inner modelwith a Woodin cardinal, then K^M \| delta is universal for all mice in V ofcardinality less than delta.

Downward transference of mice and universality of local core models