A dichotomy on Schreier sets
Volume 132 / 1999
Studia Mathematica 132 (1999), 245-256
DOI: 10.4064/sm-132-3-245-256
Abstract
We show that the Schreier sets 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 and F ⊂ N } ⊆ S_α.