A dichotomy on Schreier sets

Judd, Robert

Judd, Robert

Studia Mathematica, Tome 133 (1999), p. 245-256 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $M = {(m_{i})}_{i = 1}^{\infty} \subseteq ℕ$ such that $S_{α} (M) = m_{i} : i \in E : E \in S_{α} \subseteq ℱ$ , or there exist infinite $M = {(m_{i})}_{i = 1}^{\infty}, N \subseteq ℕ$ such that $ℱ [N] (M) = m_{i} : i \in F : F \in ℱ a n d F \subset N \subseteq S_{α}$ .

Publié le : 1999-01-01

Zbl 0938.46015

EUDML-ID : urn:eudml:doc:216598

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     author = {Robert Judd},
     title = {A dichotomy on Schreier sets},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {245-256},
     zbl = {0938.46015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i3p245bwm}
}

Judd, Robert. A dichotomy on Schreier sets. Studia Mathematica, Tome 133 (1999) pp. 245-256. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i3p245bwm/

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