Thomas F. Kent

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For any enumeration degree a let D s a be the set of s-degrees contained in a. We answer an open question of Watson by showing that if a is a nontrivial Σ 0 2-enumeration degree, then D s a has no least element. We also show that every countable partial order embeds into D s a .
We show that the first order theory of the Σ 0 2 s-degrees is undecidable. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π 0 2 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the Σ 0 2 s-degrees yields a new proof of the known fact (due to Downey, LaForte(More)
For any enumeration degree a let D s a be the set of s-degrees contained in a. We answer an open question of Watson by showing that if a is a nontrivial Σ 0 2-enumeration degree, then D s a has no least element. We also show that every countable partial order embeds into D s a. Finally, we construct Σ 0 2-sets A and B such that B ≤ e A but for every X ≡ e(More)