Extended Ramsey theory for words representing rationals

Vassiliki Farmaki ¹   ; Andreas Koutsogiannis ¹

¹ Department of Mathematics Athens University Panepistemiopolis 15784 Athens, Greece

Fundamenta Mathematicae, Tome 223 (2013) no. 1, pp. 1-27

Résumé

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.

Détail

DOI : 10.4064/fm223-1-1

Keywords: ramsey theory words finite alphabet unified work carlson who presented method extend theory words infinite alphabet subject fixed dominating principle present work establish extension carlsons approach countable ordinals schreier type families developing extended ramsey theory dominated words doubly infinite alphabet omega mathbb ast located words apply theory exploiting budak pym representation rational numbers obtain analogous partition theory set rational numbers