Cupping and definability in the local structure of the enumeration degrees
Hristo Ganchev, Mariya I. Soskova · Journal of Symbolic Logic · 2012
Abstract We show that every splitting of in the local structure of the enumeration degrees, , contains at least one low-cuppable member. We apply this new structural property to show that the classes of all -pairs in , all downwards properly enumeration degrees and all upwards properly enumeration degrees are first order definable in .