Partitioning infinite hypergraphs into few monochromatic Berge-paths

Extending a result of Rado to hypergraphs, we prove that for all $s, k, t \in $\mathbb{N}$$with$k \geq t \geq 2$,theverticesofevery$r = s(k-t+1)$-edge-colouredcountablyinfinitecomplete$k$-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.