2018/01/31 by Yong Cheng, Cheng, Yong
Computer Science · Mathematics · #03E55 #03E99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · doi:10.48550/arxiv.1801.10420
openalex publication_date 2018/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that: if κ is supercompact and the HOD Hypothesis holds, then there is a proper class of regular cardinals in Vκ which are measurable in HOD. Woodin also proved this result. As a corollary, we prove Woodin's Local Universality Theorem. This work shows that under the assumption of the HOD Hypothesis and supercompact cardinals, large cardinals in V are reflected to be large cardinals in HOD in a local way, and reveals the huge difference between HOD-supercompact cardinals and supercompact cardinals under the HOD Hypothesis.