Maria L. Affatato

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We give an alternative and more informative proof that every nontrivial Σ2-enumeration degrees is the meet of two incomparable Σ 0 2-degrees, which allows us to show the stronger result that for every incomplete Σ2enumeration degree a, there exist enumeration degrees x1 and x2 such that a, x1, x2 are incomparable, and for all b ≤ a, b = (b ∪ x1) ∩ (b ∪ x2).
We show that the first order theory of the Σ2 s-degrees is undecidable. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π2 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the Σ2 s-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies)(More)
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