The theory of the recursively enumerable weak truth-table degrees is undecidable - Ambos-Spies, Klaus; Nies, André; Shore, Richard A. (The journal of symbolic logic, 1992)
We show that the partial order of -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.