Extended Ramsey theory for words representing rationals

Vassiliki Farmaki; Andreas Koutsogiannis

Fundamenta Mathematicae (2013)

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

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.