HOD in natural models of AD+

The goal of this paper is to compute the full HOD of models of AD+ of the form L(℘(R)) below “ADR+Θ is regular”. As part of this computation, we give a computation of HOD|Θ left open in [3] for Θ a successor in the Solovay sequence. Our work, when combined with [3], shows that in AD+ models of the form L(℘(R)) below “ADR+Θ is regular”, HOD satisfies GCH.