Let Dtt denote the set of truth-table degrees. A bijection π : Dtt → Dtt is an automorphism if for all truth-table degrees x and y we have x ≤tt y ⇔ π (x) ≤tt π (y). We say an automorphism π is fixed on a cone if there is a degree b such that for all x ≥tt b we have π (x) = x. We first prove that for every 2-generic real X we have X'≰tt X ⊕ 0'. We next prove that for every real X ≥tt 0' there is a real Y such that Y ⊕ 0' ≡tt Y' ≡tt X. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on a cone.
"Automorphisms of the truth-table degrees are fixed on a cone." J. Symbolic Logic 74 (2) 679 - 688, June 2009. https://doi.org/10.2178/jsl/1243948334