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Let Dtt denote the set of truth-table degrees. A bijection p from Dtt to Dttis an automorphism if for all truth-table degrees x and y we have x <=tt y ifand only if p(x) <=tt p(y). We say an automorphism p is fixed on some cone ifthere is a degree b such that for all x >=tt b we have p(x) = x. We first provethat for every 2-generic real X we have X' is not tt below X + 0'. We nextprove 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 thetruth-table degrees is fixed on some cone.

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