Determinacy of F_sigma games of length omega^2 is equivalent to existence of a transitive KP + AD model containing the reals that reflects Pi_1 facts about the next admissible set.
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$F_\sigma$ Games and Reflection in $L(\mathbb{R})$
Determinacy of F_sigma games of length omega^2 is equivalent to existence of a transitive KP + AD model containing the reals that reflects Pi_1 facts about the next admissible set.