We present a diamond principle concerning all subsets of , the supremum of the ordinals that are the surjective image of . We prove that holds in Steel’s core model , a canonical inner model for determinacy.
Daniel Cunningham. "A Diamond Principle Consistent with AD." Notre Dame J. Formal Logic 58 (3) 397 - 407, 2017. https://doi.org/10.1215/00294527-2017-0008