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A canonical Ramsey-type theorem for finite subsets of $ℕ$

Diana Piguetová — 2003

Commentationes Mathematicae Universitatis Carolinae

T. Brown proved that whenever we color $𝒫_{f} (ℕ)$ (the set of finite subsets of natural numbers) with finitely many colors, we find a monochromatic structure, called an arithmetic copy of an $ω$ -forest. In this paper we show a canonical extension of this theorem; i.eẇhenever we color $𝒫_{f} (ℕ)$ with arbitrarily many colors, we find a canonically colored arithmetic copy of an $ω$ -forest. The five types of the canonical coloring are determined. This solves a problem of T. Brown.

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A canonical Ramsey-type theorem for finite subsets of ℕ

A canonical Ramsey-type theorem for finite subsets of $ℕ$