The Jump Operator on the Ω-enumeration Degrees
نویسنده
چکیده
The jump operator on the ω-enumeration degrees is introduced in [11]. In the present paper we prove a jump inversion theorem which allows us to show that the enumeration degrees are first order definable in the structureDω ′ of the ω-enumeration degrees augmented by the jump operator. Further on we show that the groups of the automorphisms of Dω ′ and of the enumeration degrees are isomorphic. In the second part of the paper we study the jumps of the ω-enumeration degrees below 0ω ′. We define the ideal of the almost zero degrees and obtain a natural characterization of the class H of the ω-enumeration degrees below 0ω ′ which are high n for some n and of the class L of the ω-enumeration degrees below 0ω ′ which are low n for some n.
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