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

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 )
Keywords Enumeration reducibility  Semirecursive set  Branching element
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DOI 10.1007/s00153-008-0081-7
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References found in this work BETA

Computability Theory.S. Barry Cooper - 2004 - 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 Infima in the Recursively Enumerable Degrees.Theodore A. Slaman - 1991 - Annals of Pure and Applied Logic 52 (1-2):155-179.
The Density of the Nonbranching Degrees.Peter A. Fejer - 1983 - Annals of Pure and Applied Logic 24 (2):113-130.

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