### The Theory of the Recursively Enumerable Weak Truth-Table Degrees is Undecidable

Klaus Ambos-Spies, Andre Nies, and Richard A. Shore
Source: J. Symbolic Logic Volume 57, Issue 3 (1992), 864-874.

#### Abstract

We show that the partial order of $\Sigma^0_3$-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.

Full-text: Remote access
If you are a member of the ASL, log in to Euclid for access.
Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.