The theory of the recursively enumerable weak truth-table degrees is undecidable
Klaus Ambos‐Spies, André Nies, Richard A. Shore · Journal of Symbolic Logic · 1992
Abstract 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.