$F_{\sigma }$ Games and Reflection in $L(\mathbb{R})$

Abstract

It is shown that determinacy of $F_{\sigma }$ games of length ${\omega }^2$ is equivalent to the existence of a transitive model of KP + AD which contains the reals and reflects ${\Pi }_1$ facts about the next admissible set.

arXiv comment20 pages. This version: February 2019