Borel games of length ω² are determined iff for every countable ordinal α there exists a fine-structural countably iterable extender model of Zermelo set theory with α-many iterated powersets above a limit of Woodin cardinals.
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Long Borel Games
Borel games of length ω² are determined iff for every countable ordinal α there exists a fine-structural countably iterable extender model of Zermelo set theory with α-many iterated powersets above a limit of Woodin cardinals.