We give upper and lower bounds for the strength of ordinal definable determinacy in a small admissible set. The upper bound is roughly a premouse with a measurable cardinal of Mitchell order and successors. The lower bound are models of ZFC with sequences of measurable cardinals, extending the work of Lewis, below a regular limit of measurable cardinals.
"Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets." Notre Dame J. Formal Logic 53 (3) 351 - 371, 2012. https://doi.org/10.1215/00294527-1716766