Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets
Diego Rojas‐Rebolledo · Notre Dame Journal of Formal Logic · 2012
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 κ of Mitchell order κ++ and ω 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.