No, the codomain of gamma is the set of (distributions over) consequences.
Hammond’s notation is inspired by the Savage framework in which states and consequences are distinct. Savage thinks of a consequence as the result of behaviour or action in some state, though this isn’t so intuitively applicable in the case of decision trees. I included it for completeness but I don’t use the gamma function explicitly anywhere.
Is the idea that the set of “states” is the codomain of gamma?
No, the codomain of gamma is the set of (distributions over) consequences.
Hammond’s notation is inspired by the Savage framework in which states and consequences are distinct. Savage thinks of a consequence as the result of behaviour or action in some state, though this isn’t so intuitively applicable in the case of decision trees. I included it for completeness but I don’t use the gamma function explicitly anywhere.