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Downward transference of mice and universality of local core models
If M is a proper class inner model of ZFC and omega_2^M=omega_2, then every
sound 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 is
universal for all countable mice in V.
Similarly, if M is a proper class inner model of ZFC, delta>omega_1 is
regular, (delta^+)^M = delta^+, and in V there is no proper class inner model
with a Woodin cardinal, then K^M \| delta is universal for all mice in V of
cardinality less than delta.Comment: Revised version, incorporating the referee's suggestion
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