A Covering Lemma for HOD of K (ℝ)

Notre Dame Journal of Formal Logic 51 (4):427-442 (2010)
Abstract
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
Keywords descriptive set theory   determinacy   fine structure
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