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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DOI 10.1215/00294527-2010-027
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References found in this work BETA

The Real Core Model and its Scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.
Is There a Set of Reals Not in K?Daniel W. Cunningham - 1998 - Annals of Pure and Applied Logic 92 (2):161-210.
A Covering Lemma for L(ℝ).Daniel W. Cunningham - 2002 - Archive for Mathematical Logic 41 (1):49-54.
A Covering Lemma for $${K}$$.Daniel W. Cunningham - 2007 - Archive for Mathematical Logic 46 (3):197-221.

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