A canonical Ramsey-type theorem for finite subsets of
Commentationes Mathematicae Universitatis Carolinae (2003)
- Volume: 44, Issue: 2, page 235-243
- ISSN: 0010-2628
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topPiguetová, Diana. "A canonical Ramsey-type theorem for finite subsets of $\mathbb {N}$." Commentationes Mathematicae Universitatis Carolinae 44.2 (2003): 235-243. <http://eudml.org/doc/249205>.
@article{Piguetová2003,
abstract = {T. Brown proved that whenever we color $\mathcal \{P\}_\{f\} (\mathbb \{N\})$ (the set of finite subsets of natural numbers) with finitely many colors, we find a monochromatic structure, called an arithmetic copy of an $\omega $-forest. In this paper we show a canonical extension of this theorem; i.eẇhenever we color $\mathcal \{P\}_\{f\}(\mathbb \{N\})$ with arbitrarily many colors, we find a canonically colored arithmetic copy of an $\omega $-forest. The five types of the canonical coloring are determined. This solves a problem of T. Brown.},
author = {Piguetová, Diana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {canonical coloring; forests; van der Waerden's theorem; arithmetic progression; canonical coloring; forests; van der Waerden's theorem; arithmetic progression},
language = {eng},
number = {2},
pages = {235-243},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A canonical Ramsey-type theorem for finite subsets of $\mathbb \{N\}$},
url = {http://eudml.org/doc/249205},
volume = {44},
year = {2003},
}
TY - JOUR
AU - Piguetová, Diana
TI - A canonical Ramsey-type theorem for finite subsets of $\mathbb {N}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 2
SP - 235
EP - 243
AB - T. Brown proved that whenever we color $\mathcal {P}_{f} (\mathbb {N})$ (the set of finite subsets of natural numbers) with finitely many colors, we find a monochromatic structure, called an arithmetic copy of an $\omega $-forest. In this paper we show a canonical extension of this theorem; i.eẇhenever we color $\mathcal {P}_{f}(\mathbb {N})$ with arbitrarily many colors, we find a canonically colored arithmetic copy of an $\omega $-forest. The five types of the canonical coloring are determined. This solves a problem of T. Brown.
LA - eng
KW - canonical coloring; forests; van der Waerden's theorem; arithmetic progression; canonical coloring; forests; van der Waerden's theorem; arithmetic progression
UR - http://eudml.org/doc/249205
ER -
References
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