A superhigh diamond in the c.e. tt-degrees

Archive for Mathematical Logic 50 (1-2):33-44 (2011)

Abstract
The notion of superhigh computably enumerable (c.e.) degrees was first introduced by (Mohrherr in Z Math Logik Grundlag Math 32: 5–12, 1986) where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in (Proc Amer Math Soc 94:123–128, 1985) that the diamond lattice can be embedded into the c.e. tt-degrees preserving 0 and 1 and that the two atoms can be low. In this paper, we prove that the two atoms in such embeddings can also be superhigh
Keywords Computably enumerable sets  Truth-table degrees  Superhighness  Lattice embeddings
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DOI 10.1007/s00153-010-0198-3
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References found in this work BETA

Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
A Refinement of Lown and Highn for the R.E. Degrees.Jeanleah Mohrherr - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (1-5):5-12.
A Refinement of Low N and High N for the R.E. Degrees.Jeanleah Mohrherr - 1986 - Mathematical Logic Quarterly 32 (1‐5):5-12.
On Very High Degrees.Keng Meng Ng - 2008 - Journal of Symbolic Logic 73 (1):309-342.

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