For α, β, n ordinals α → (β, n) means that any graph on the ordinal α either contains an independent set of order-type β or a complete subgraph of order-type n. We only consider cases where n is a natural number, hence the naming. The partition relation α → (β, n) for α, β finite multiples of κ where κ = ω or κ is weakly compact is characterized by a finitary problem as is the same for α, β fin...