Π12 Wadge degrees Original Research Article

Suppose that any two Π12 sets are comparable in the sense of Wadge degrees. Then every real has a dagger. This argument proceeds by using the Dodd-Jensen core model theory to show that ∀ x ϵ ωω(x#Ð) along with, say, “0† implies the existence of a Π12 norm of length u2. As a result of more recent work by John Steel, the same argument will extend to show that the Wadge comparability of all Π12 sets implies Π12 determinacy.