# 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, $$\mathbf 0^{(4)}$$.
1 Citations
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.

## References

SHOWING 1-10 OF 30 REFERENCES

• Mathematics
• 1977
It is shown that any jump preserving order automorphismF of the degrees of unsolvability must satisfyF(c) = c for all degreesc≧0(4). The proof uses a result on initial segments of degrees in
We characterize the isomorphism types of principal ideals of the Turing degrees below 0′ that are lattices as the lattices that have a Σ3 presentation.
Abstract Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of
It is shown that for every 2-generic real X the authors have X′ ≰ttX ⊕ 0′ and this is used to demonstrate that every automorphism of the truth-table degrees is fixed on a cone.
• Mathematics
• 2002
We characterize the isomorphism types of principal ideals of the Turing degrees below 0′ that are lattices as the lattices with a S03 presentation, by showing that each S03 -presentable bounded upper
• Mathematics
Journal of Symbolic Logic
• 1976
A complete characterization of the order types of the countable initial segments of the degrees of unsolvability is given by proving the following theorem: any countable upper semilattice with least element can be embedded as an initial segment of thedegree.
This work answers two questions from the topic of degrees of unsolvability, which is part of recursive function theory. We give a simple and explicit example of elementary inequivalence of the Turing
• Mathematics
• 2003
Preface Acknowledgements Foreword Introduction 1. A primer on ordered sets and lattices 2. Order theory of domains 3. The Scott topology 4. The Lawson Topology 5. Morphisms and functors 6. Spectral
Degree theory, that is the study of the structure of the Turing degrees (or degrees of unsolvability) has been divided by Simpson [24; §5] into two parts—global and local. By the global theory he
• R. Shore
• Mathematics
Journal of Symbolic Logic
• 1982
Relativization—the principle that says one can carry over proofs and theorems about partial recursive functions and Turing degrees to functions partial recursive in any given set A and the Turing