# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Extended Ramsey theory for words representing rationals

### Tom 223 / 2013

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

#### Streszczenie

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.

#### Autorzy

• 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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