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arXiv · 0805.0005

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

Bernard A. Anderson
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Abstract

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.

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Bernard A. Anderson. 2008-07-19. Automorphisms of the truth-table degrees are fixed on some cone. https://arxiv.org/abs/0805.0005

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