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 ω-ℤ*-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-1,
author = {Vassiliki Farmaki and Andreas Koutsogiannis},
title = {Extended Ramsey theory for words representing rationals},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {1-27},
zbl = {1284.05326},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-1}
}
Vassiliki Farmaki; Andreas Koutsogiannis. Extended Ramsey theory for words representing rationals. Fundamenta Mathematicae, Tome 220 (2013) pp. 1-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-1/