 Homogeneous set for a colouring

For a colouring $\chi :[S{]}^r\to \{0,\dots ,k-1\}$ of the $r$-element subsets of a set $S$, a subset $H\subseteq S$ is homogeneous if all its $r$-element subsets receive the same colour. The infinite Ramsey theorem for r-sets guarantees an infinite homogeneous subset when $S=\mathbb{N}$, $r$ is positive and the number of colours is finite. This does not guarantee a computable set when the colouring is computable.