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

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

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Citations of this work

Bounded-low sets and the high/low hierarchy.Huishan Wu - 2020 - Archive for Mathematical Logic 59 (7-8):925-938.

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References found in this work

Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
A Refinement of Low n_ and High _n for the R.E. Degrees.Jeanleah Mohrherr - 1986 - Mathematical Logic Quarterly 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.

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