Year: 2026
Type: preprint
Abstract: We identify a class of simple yet nontrivial forcing notions that preserve the Ultrapower Axiom (UA) over canonical inner models, reaching the level of a strong cardinal. The forcings we consider are discrete product forcings whose index sets are chosen and spaced according to the structure of the underlying nonoverlapping extender sequence. As an application, we show that UA is consistent with the existence of a strong cardinal $κ$ such that $V\neq \text{HOD}_X$ for every $X\in V_κ$, answering a question of Goldberg.
Source: arXiv (Cornell University)
Author: Kaplan, Eyal
Institution: Carnegie Mellon University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211988718