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Sabok showed that the set of codes for G_δ Ramsey positive subsets of [ω]^ω is Σ¹₂-complete. We extend this result by providing sufficient conditions for the set of codes for G_δ Ramsey positive subsets of an arbitrary topological Ramsey space to be Σ¹₂-complete.
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Allison Wang (2024) studied this question.
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