Subtlety and partition relations

We study the subtlety of a cardinal κ and of ^kΛ. We show that, under a certain large cardinal assumption, it is consistent that ^kΛ is subtle for some Λ > κ but κ is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of P^kΛ can be characterized by a certain partition relation on ^kΛ. We also study the property of faintness of κ, and the subtlety of ^kΛ with the strong inclusion.