## Journal of Symbolic Logic

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

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 57, Issue 3 (1992), 864-874.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744045

Mathematical Reviews number (MathSciNet)
MR1187453

Zentralblatt MATH identifier
0776.03020

JSTOR