Extended Ramsey theory for words representing rationals

Volume 223 / 2013

Vassiliki Farmaki, Andreas Koutsogiannis Fundamenta Mathematicae 223 (2013), 1-27 MSC: Primary 05C55; Secondary 05A18, 05A05. DOI: 10.4064/fm223-1-1

Abstract

Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for $\omega $-$\mathbb {Z}^\ast $-located words), and we apply this theory, exploiting the Budak–Işik–Pym representation of rational numbers, to obtain an analogous partition theory for the set of rational numbers.

Authors

  • Vassiliki FarmakiDepartment of Mathematics
    Athens University
    Panepistemiopolis
    15784 Athens, Greece
    e-mail
  • Andreas KoutsogiannisDepartment of Mathematics
    Athens University
    Panepistemiopolis
    15784 Athens, Greece
    e-mail

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