Prefix-independent Σ₀² objectives with neutral letters are positional over arbitrary graphs exactly when recognized by history-deterministic monotone co-Büchi automata over countable ordinals, with proofs for mean-payoff positionality and a completeness lifting from finite graphs.
16 Hugo Gimbert and Wiesław Zielonka
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Positionality in $\Sigma_0^2$ and a completeness result
Prefix-independent Σ₀² objectives with neutral letters are positional over arbitrary graphs exactly when recognized by history-deterministic monotone co-Büchi automata over countable ordinals, with proofs for mean-payoff positionality and a completeness lifting from finite graphs.