The <partition relation> $\kappa\to(\lambda)^\alpha_\beta$ means that for every coloring $c:[\kappa]^\alpha\to\beta$, there is $H\subseteq\kappa$ with $|H|=\lambda$ such that $c$ is constant on $[H]^\alpha$. Here $[X]^\alpha$ denotes the <subsets> of $X$ of <cardinality> $\alpha$, and the subscript is the number of colors. \b[The domain consists of <subsets> of size $\alpha$, not ordered tuples], and the definition also makes sense for infinite arity.

Solution

Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 19 / 4 / i / a / Solution

 Solution (source code)