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On Cupping and Ahmad Pairs
Journal of Symbolic Logic:1-12 (forthcoming)
Abstract
Working toward showing the decidability of the $\forall \exists $ -theory of the ${\Sigma ^0_2}$ -enumeration degrees, we prove that no so-called Ahmad pair of ${\Sigma ^0_2}$ -enumeration degrees can join to ${\mathbf 0}_e'$.Author's Profile
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References found in this work
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.
On extensions of embeddings into the enumeration degrees of the -sets.Steffen Lempp, Theodore A. Slaman & Andrea Sorbi - 2005 - Journal of Mathematical Logic 5 (02):247-298.
Interpreting true arithmetic in the local structure of the enumeration degrees.Hristo Ganchev & Mariya Soskova - 2012 - Journal of Symbolic Logic 77 (4):1184-1194.
The Π₃-Theory of the [image] -Enumeration Degrees Is Undecidable.Thomas F. Kent - 2006 - Journal of Symbolic Logic 71 (4):1284 - 1302.
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