Cupping and noncupping in the enumeration degrees of ∑20 sets

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Cupping and noncupping in the enumeration

We prove the following three theorems on the enumeration degrees of Σ2 sets. Theorem A: There exists a nonzero noncuppable Σ 0 2 enumeration degree. Theorem B: Every nonzero ∆2 enumeration degree is cuppable to 0e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low ∆2 enumeration degree with the anticupping property.

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We prove that no subclass of the Σ 2 enumeration degrees containing the 3-c.e. enumeration degrees can be cupped to 0e by a single Σ 2 enumeration degree.

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Cupping D20 Enumeration Degrees to 0 e '

In this paper we prove that every nonzero ∆2 e-degree is cuppable to 0e by a 1-generic ∆ 0 2 e-degree (so low and nontotal) and that every nonzero ω-c.e. e-degree is cuppable to 0e by an incomplete

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The limitations of cupping in the local structure of the enumeration degrees

We prove that a sequence of sets containing representatives of cupping partners for every nonzero ∆2 enumeration degree cannot have a ∆ 0 2 enumeration. We also prove that no subclass of the Σ 2 enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to 0e by a single incomplete Σ 2 enumeration degree.

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 1996

ISSN: 0168-0072

DOI: 10.1016/s0168-0072(96)00009-7