Downward transference of mice and universality of local core models
Logic
2019-02-11 v2
Abstract
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.
Cite
@article{arxiv.1204.1006,
title = {Downward transference of mice and universality of local core models},
author = {Andrés Eduardo Caicedo and Martin Zeman},
journal= {arXiv preprint arXiv:1204.1006},
year = {2019}
}
Comments
Revised version, incorporating the referee's suggestions