Automorphisms of the truth-table degrees are fixed on some cone
Bernard A. Anderson

TL;DR
This paper proves that all automorphisms of the truth-table degrees are fixed on some cone, using properties of 2-generic reals and the relationship between degrees and jumps.
Contribution
It establishes that every automorphism of the truth-table degrees is fixed on some cone, advancing understanding of their structural rigidity.
Findings
Automorphisms are fixed on some cone for all truth-table degrees.
Properties of 2-generic reals are used to analyze automorphisms.
Relationships between degrees and jumps are characterized.
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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Taxonomy
TopicsComputability, Logic, AI Algorithms · Digital Image Processing Techniques · semigroups and automata theory
