A dichotomy on Schreier sets

1997/06/05 by Robert Judd, Judd, Robert
Mathematics · #05D10 #46B #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:05D10 #msc:46B

paper · pdf · doi:10.48550/arxiv.math/9706209

arxiv created 1997/06/05 · arxiv updated 2016/09/07

Abstract

We show that the Schreier sets S_α (α<ω₁) satisfy the following dichotomy property. For every hereditary collection \cf of finite subsets of \N, either there exists infinite M=(m_i)₁^∞⊆\N such that \cs_α(M)=\\m_i:i∈ E\:E∈\cs_α\⊆\cf, or there exist infinite M=(m_i)₁^∞,N⊆\N such that \cf[N](M)=\\m_i:i∈ F\:F∈\cf and F⊂ N\⊆\cs_α.

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