The theory of the recursively enumerable weak truth-table degrees is undecidable

Journal of Symbolic Logic 57 (3):864-874 (1992)
We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi
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DOI 10.2307/2275436
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E. Herrmann (1997). Boolean Pairs Formed by the Δn0-Sets. Annals of Pure and Applied Logic 87 (2):145-149.
Kejia Ho & Frank Stephan (2002). Classes Bounded by Incomplete Sets. Annals of Pure and Applied Logic 116 (1-3):273-295.

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