Undecidability of local structures of s-degrees and Q-degrees

نویسندگان

  • Maria Libera Affatato
  • Thomas F. Kent
  • Andrea Sorbi
چکیده

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) that the first order theory of the c.e. Q-degrees is undecidable.

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تاریخ انتشار 2007