A Rigid Cone in the Truth-Table Degrees with Jump

@inproceedings{KjosHanssen2009ARC,
  title={A Rigid Cone in the Truth-Table Degrees with Jump},
  author={Bj{\o}rn Kjos-Hanssen},
  booktitle={Computability and Complexity},
  year={2009}
}
  • B. Kjos-Hanssen
  • Published in Computability and Complexity 26 January 2009
  • Education, Mathematics
The automorphism group of the truth-table degrees with order and jump is fixed on the set of degrees above the fourth jump, \(\mathbf 0^{(4)}\). 
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PERMUTATIONS OF THE INTEGERS INDUCE ONLY THE TRIVIAL AUTOMORPHISM OF THE TURING DEGREES

It is shown that a permutation of \(\omega \) cannot induce any nontrivial automorphism of the Turing degrees of members ofMembers of \(2^{\omega }\), and in fact any permutation that induces the trivial Automorphism must be computable.

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