The Π₃-Theory of the [image] -Enumeration Degrees Is Undecidable

Journal of Symbolic Logic 71 (4):1284 - 1302 (2006)
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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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Strong minimal pairs in the enumeration degrees.Josiah Jacobsen-Grocott - 2024 - Annals of Pure and Applied Logic 175 (10):103464.

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References found in this work

Enumeration reducibility and partial degrees.John Case - 1971 - Annals of Mathematical Logic 2 (4):419-439.
Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Definability in the enumeration degrees.Theodore A. Slaman & W. Hugh Woodin - 1997 - Archive for Mathematical Logic 36 (4-5):255-267.
Some Special Pairs of Σ2 e-Degrees.Seema Ahmad & Alistair H. Lachlan - 1998 - Mathematical Logic Quarterly 44 (4):431-449.

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