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The Π₃-Theory of the $\Sigma _{2}^{0}$ -Enumeration Degrees Is Undecidable

Thomas F. Kent
The Journal of Symbolic Logic
Vol. 71, No. 4 (Dec., 2006), pp. 1284-1302
Stable URL: http://www.jstor.org/stable/27588513
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Π₃-Theory of the
          $\Sigma _{2}^{0}$
          -Enumeration Degrees Is Undecidable
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Abstract

We show that in the language of {≤}, the Π₃-fragment of the first order theory of the $\Sigma _{2}^{0}$-enumeration degrees is undecidable. We then extend this result to show that the Π₃-theory of any substructure of the enumeration degrees which contains the $\Delta _{2}^{0}$-degrees is undecidable.

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