Some combinatorics involving $\xi $-large sets

Volume 175 / 2002

Teresa Bigorajska, Henryk Kotlarski Fundamenta Mathematicae 175 (2002), 119-125 MSC: Primary 05A18. DOI: 10.4064/fm175-2-2

Abstract

We prove a version of the Ramsey theorem for partitions of (increasing) $n$-tuples. We derive this result from a version of König's infinity lemma for $\xi $-large trees. Here $\xi <\varepsilon _ 0$ and the notion of largeness is in the sense of Hardy hierarchy.

Authors

  • Teresa BigorajskaFaculty of Mathematics
    Cardinal Stefan Wyszyński University
    Dewajtis 5, 01-815 Warszawa, Poland
    e-mail
  • Henryk KotlarskiFaculty of Mathematics
    Cardinal Stefan Wyszyński University
    Dewajtis 5, 01-815 Warszawa, Poland
    and
    Institute of Mathematics
    Academy of Podlasie
    08-110 Siedlce, Poland
    e-mail

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