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On supersets of non-low sets
Journal of Symbolic Logic 86 (3):1282-1292 (2021)
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.Other Versions
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References found in this work
Classes of Recursively Enumerable Sets and Degrees of Unsolvability.Donald A. Martin - 1966 - Mathematical Logic Quarterly 12 (1):295-310.
Degrees of recursively enumerable sets which have no maximal supersets.A. H. Lachlan - 1968 - Journal of Symbolic Logic 33 (3):431-443.
Degree theoretic definitions of the low2 recursively enumerable sets.Rod Downey & Richard A. Shore - 1995 - Journal of Symbolic Logic 60 (3):727 - 756.
Automorphisms of the lattice of recursively enumerable sets. Part II: Low sets.Robert I. Soare - 1982 - Annals of Mathematical Logic 22 (1):69.
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