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