A dichotomy on Schreier sets

• Autorzy: Robert Judd
• Języki publikacji: EN

Abstrakty

EN

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 $ℱ[N](M) = {{m_i:i ∈ F}:F ∈ ℱ and F ⊂ N } ⊆ S_α$.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 05D10: Ramsey theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 3
• Strony: 245-256

Daty

wydano

1999

otrzymano

1997-09-08

Twórcy

autor

Robert Judd

• Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613, U.S.A.

Bibliografia

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