Downward Transference of Mice and Universality of Local Core Models

Authors

Andrés Eduardo Caicedo, Boise State University
Martin Zeman, University of California at Irvine

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, K^Mǁω₂ 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 K^Mǁδ is universal for all mice in V of cardinality less than δ.

Publication Information

Caicedo, Andrés Eduardo and Zeman, Martin. (2017). "Downward Transference of Mice and Universality of Local Core Models". The Journal of Symbolic Logic, 82(2), 385-419. https://doi.org/10.1017/jsl.2016.68