THE GROUND AXIOM IS CONSISTENT WITH V ≠ HOD

摘要: The Ground Axiom asserts that the universe is not a nontrivial set-forcing extension of any inner model. Despite apparent second-order nature this assertion, it first-order expressible in set theory. previously known models all satisfy strong forms V = HOD. In article, we show relatively consistent with ≠ fact, every model ZFC has class-forcing + GA method accommodates large cardinals: supercompact cardinal, for example, HOD which cardinal preserved.