Working in ZF+AD alone, we prove that every set of ordinals with cardinality at least Θ can be covered by a set of ordinals in HOD of K(ℝ) of the same cardinality, when there is no inner model with an ℝ-complete measurable cardinal. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.
"A Covering Lemma for HOD of K(ℝ)." Notre Dame J. Formal Logic 51 (4) 427 - 442, 2010. https://doi.org/10.1215/00294527-2010-027