Computable colouring
= Computable colouring
{title2=$\chi:[\mathbb N]^r\to k$}
A colouring is computable when an <algorithm> sorts the finite input subset, computes its colour and terminates. Its colour classes are uniformly <computable sets>. The distinction between existence of an infinite <homogeneous set for a colouring> and effective construction of one is a basic phenomenon in <computability theory>.