The theory of the metarecursively enumerable degrees

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Journal of Mathematical Logic 6 (1):49-68 (2006)
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Abstract

Sacks [23] asks if the metarecursively enumerable degrees are elementarily equivalent to the r.e. degrees. In unpublished work, Slaman and Shore proved that they are not. This paper provides a simpler proof of that result and characterizes the degree of the theory as [Formula: see text] or, equivalently, that of the truth set of [Formula: see text].

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10.1142/s0219061306000505

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References found in this work

On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
Metarecursive sets.G. Kreisel & Gerald E. Sacks - 1965 - Journal of Symbolic Logic 30 (3):318-338.
Finite injury and Σ1-induction.Michael Mytilinaios - 1989 - Journal of Symbolic Logic 54 (1):38 - 49.
Degrees of Unsolvability.Gerald E. Sacks - 1966 - Princeton University Press.
Metarecursively enumerable sets and their metadegrees.Graham C. Driscoll - 1968 - Journal of Symbolic Logic 33 (3):389-411.

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