Displaying similar documents to “On game-theoretic methods in the theory of Souslin sets”

A dichotomy on Schreier sets

Robert Judd (1999)

Studia Mathematica

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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 ∞ ⊆ ℕ such that S α ( M ) = m i : i ∈ E : E ∈ S α ⊆ ℱ , or there exist infinite M = ( m i ) i = 1 ∞ , N ⊆ ℕ such that ℱ [ N ] ( M ) = m i : i ∈ F : F ∈ ℱ a n d F ⊂ N ⊆ S α .