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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The first author would like to thank her advisor, Andrea Sorbi, whose guidance made this paper possible. The second author has been supported by a Marie Curie Incoming International Fellowship of the European Community FP6 Program under contract number MIFI-CT-2006-021702.
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Affatato, M.L., Kent, T.F. & Sorbi, A. Branching in the \({\Sigma^0_2}\) -enumeration degrees: a new perspective. Arch. Math. Logic 47, 221–231 (2008). https://doi.org/10.1007/s00153-008-0081-7
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DOI: https://doi.org/10.1007/s00153-008-0081-7