The n-r.E. Degrees: Undecidability and σ1 substructures

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Journal of Mathematical Logic 12 (1):1250005- (2012)
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Abstract

We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].

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10.1142/s0219061312500055

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Citations of this work

Isolated maximal d.r.e. degrees.Yong Liu - 2019 - Annals of Pure and Applied Logic 170 (4):515-538.

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References found in this work

Limiting recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
Systems of Logic Based on Ordinals.Andrzej Mostowski - 1939 - Journal of Symbolic Logic 4 (3):128-129.
A minimal pair of recursively enumerable degrees.C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (2):159-168.

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