  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' is not tt below 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 some cone.
