Extended Ramsey theory for words representing rationals

Vassiliki Farmaki; Andreas Koutsogiannis

Extended Ramsey theory for words representing rationals

Vassiliki Farmaki; Andreas Koutsogiannis

Fundamenta Mathematicae (2013)

Volume: 223, Issue: 1, page 1-27
ISSN: 0016-2736

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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.

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Vassiliki Farmaki, and Andreas Koutsogiannis. "Extended Ramsey theory for words representing rationals." Fundamenta Mathematicae 223.1 (2013): 1-27. <http://eudml.org/doc/283036>.

@article{VassilikiFarmaki2013,
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 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.},
author = {Vassiliki Farmaki, Andreas Koutsogiannis},
journal = {Fundamenta Mathematicae},
keywords = {partition theorems; --located words; rational numbers; Schreier families},
language = {eng},
number = {1},
pages = {1-27},
title = {Extended Ramsey theory for words representing rationals},
url = {http://eudml.org/doc/283036},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Vassiliki Farmaki
AU - Andreas Koutsogiannis
TI - Extended Ramsey theory for words representing rationals
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 1
SP - 1
EP - 27
AB - 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.
LA - eng
KW - partition theorems; --located words; rational numbers; Schreier families
UR - http://eudml.org/doc/283036
ER -

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