The ground axiom is consistent with V $\neq $ HOD
The ground axiom is consistent with V $\neq $ HOD
The Ground Axiom asserts that the universe is not a nontrivial set-forcing extension of any inner model. Despite the apparent second-order nature of this assertion, it is first-order expressible in set theory. The previously known models of the Ground Axiom all satisfy strong forms of $V=\mathrm {HOD}$. In this article, …