Abstract
Suppose that any two Π 1 2 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 ω ω(x #Ð) along with, say, “0 † implies the existence of a Π 1 2 norm of length u 2. As a result of more recent work by John Steel, the same argument will extend to show that the Wadge comparability of all Π 1 2 sets implies Π 1 2 determinacy.
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