Partitioning Infinite Hypergraphs into Few Monochromatic Berge-Paths

Extending a result of Rado to hypergraphs, we prove that for all s, k, t ∈ℕ with k ≥ t ≥ 2 , the vertices of every r = s(k-t+1) -edge-coloured countably infinite complete k -graph can be partitioned into the cores of at most s monochromatic t -tight Berge-paths of different colours. We further describe a construction showing that this result is best possible.