# A canonical Ramsey-type theorem for finite subsets of $\mathbb{N}$

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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