Branching in the $${\Sigma^0_2}$$ -enumeration degrees: a new perspective [Book Review]

Archive for Mathematical Logic 47 (3):221-231 (2008)
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Abstract

We give an alternative and more informative proof that every incomplete ${\Sigma^{0}_{2}}$ -enumeration degree is the meet of two incomparable ${\Sigma^{0}_{2}}$ -degrees, which allows us to show the stronger result that for every incomplete ${\Sigma^{0}_{2}}$ -enumeration degree a, there exist enumeration degrees x 1 and x 2 such that a, x 1, x 2 are incomparable, and for all b ≤ a, b = (b ∨ x 1 ) ∧ (b ∨ x 2 )

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References found in this work

Computability Theory.S. Barry Cooper - 2003 - Chapman & Hall.
Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
The density of the nonbranching degrees.Peter A. Fejer - 1983 - Annals of Pure and Applied Logic 24 (2):113-130.
The density of infima in the recursively enumerable degrees.Theodore A. Slaman - 1991 - Annals of Pure and Applied Logic 52 (1-2):155-179.

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