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Isolation in the CEA hierarchy

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Abstract.

Examining various kinds of isolation phenomena in the Turing degrees, I show that there are, for every n>0, (n+1)-c.e. sets isolated in the n-CEA degrees by n-c.e. sets below them. For n≥1 such phenomena arise below any computably enumerable degree, and conjecture that this result holds densely in the c.e. degrees as well. Surprisingly, such isolation pairs also exist where the top set has high degree and the isolating set is low, although the complete situation for jump classes remains unknown.

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  1. Computer Science Department, University of West Florida, 11000, University Parkway, Pensacola, FL, USA

    Geoffrey LaForte

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LaForte, G. Isolation in the CEA hierarchy. Arch. Math. Logic 44, 227–244 (2005). https://doi.org/10.1007/s00153-004-0250-2

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