On game-theoretic methods in the theory of Souslin sets

Ashok Maitra

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Robert Judd (1999)

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We show that the Schreier sets $S_{α} (α < ω_{1})$ have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite $M = {(m_{i})}_{i = 1}^{\infty} \subseteq ℕ$ such that $S_{α} (M) = m_{i} : i \in E : E \in S_{α} \subseteq ℱ$ , or there exist infinite $M = {(m_{i})}_{i = 1}^{\infty}, N \subseteq ℕ$ such that $ℱ [N] (M) = m_{i} : i \in F : F \in ℱ a n d F \subset N \subseteq S_{α}$ .

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