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

  • Bernard A. Anderson (a1)

Abstract

Let Dtt denote the set of truth-table degrees. A bijection π: DttDtt is an automorphism if for all truth-table degrees x and y we have xttyπ(x)ttπ(y). We say an automorphism π is fixed on a cone if there is a degree b such that for all xttb we have π(x) = x. We first prove that for every 2-generic real X we have X′ttX ⊕ 0′. We next prove that for every real Xtt 0′ there is a real Y such that Y ⊕ 0′ ≡ttY′ ≡ttX. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on a cone.

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References

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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