Title

Downward Transference of Mice and Universality of Local Core Models

Document Type

Article

Publication Date

6-2017

Comments

Abstract

If M is a proper class inner model of ZFC and , then every sound mouse projecting to ω and not past 0 belongs to M. In fact, under the assumption that 0 does not belong to M, KMǁω2 is universal for all countable mice in V.

Similarly, if M is a proper class inner model of ZFC, δ > ω1 is regular, (δ +) M = δ + and in V there is no proper class inner model with a Woodin cardinal, then KMǁδ is universal for all mice in V of cardinality less than δ.

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