A Dichotomy on Schreier Sets
نویسنده
چکیده
We show that the Schreier sets Sα (α < ω1) satisfy the following dichotomy property. For every hereditary collection F of finite subsets of N, either there exists infinite M = (mi)1 ⊆ N such that Sα(M) = {{mi : i ∈ E} : E ∈ Sα} ⊆ F , or there exist infinite M = (mi)1 , N ⊆ N such that F [N ](M) = {{mi : i ∈ F} : F ∈ F and F ⊂ N} ⊆ Sα.
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