Downward transference of mice and universality of local core models

Details Downward transference of mice and universality of local core models Downward transference of mice and universality of local core models

2012-04-04

arxiv.org/abs/1204.1006v1

Mathematics

Logic

37 pages

Scientific paper

If M is an inner model 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 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.

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