Extended Ramsey theory for words representing rationals
Volume 223 / 2013
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 -\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.