On supersets of non-low sets

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Journal of Symbolic Logic 86 (3):1282-1292 (2021)
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Abstract

We solve a longstanding question of Soare by showing that if ${\mathbf d}$ is a non-low $_2$ computably enumerable degree then ${\mathbf d}$ contains a c.e. set with no r-maximal c.e. superset.

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10.1017/jsl.2021.72

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