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