Paper detail

Automorphisms of the truth-table degrees are fixed on some cone

Let Dtt denote the set of truth-table degrees. A bijection p from Dtt to Dtt is an automorphism if for all truth-table degrees x and y we have x <=tt y if and only if p(x) <=tt p(y). We say an automorphism p is fixed on some cone if there is a degree b such that for all x >=tt b we have p(x) = x. We first prove that for every 2-generic real X we have X&#39; is not tt below X + 0&#39;. We next prove that for every real X >=tt 0&#39; there is a real Y such that Y + 0&#39; =tt Y&#39; =tt X. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on some cone.