= Winning-position attractor in an infinite game
{title2=$W_\alpha$}
Start with positions whose entire extension <cylinder set> lies in the winning <open set>. At each successor stage add I-positions with some successor already present and II-positions with every successor already present; take unions at limit <ordinals>. The stable set is the least <fixed point> of this <order-preserving> operation. The first entry <ordinal> supplies a strictly decreasing rank until the winning prefix is reached.
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