Choice characterization of quasideterminacy
= Choice characterization of quasideterminacy
For every move set $M$, the statement that every quasidetermined subset of $M^\omega$ is determined is equivalent in ZF to $\mathsf{AC}_{M^{<\omega}}(M)$. The forward direction encodes an arbitrary family of nonempty subsets of $M$ into a quasidetermined game; the reverse direction chooses one move from each value of a winning quasistrategy.