Undecidability of local structures of s-degrees and Q-degrees
Maria L. Affatato, Thomas F. Kent, Andrea Sorbi · 2008
We show that the first order theory of the Σ02 s-degrees is undecid-able. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π02 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the Σ02 s-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies) that the first order theory of the c.e. Q-degrees is undecidable.