# 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} }

The automorphism group of the truth-table degrees with order and jump is fixed on the set of degrees above the fourth jump, \(\mathbf 0^{(4)}\).

## One Citation

### PERMUTATIONS OF THE INTEGERS INDUCE ONLY THE TRIVIAL AUTOMORPHISM OF THE TURING DEGREES

- MathematicsThe Bulletin of Symbolic Logic
- 2018

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

### Fixed points of jump preserving automorphisms of degrees

- 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…

### LATTICE INITIAL SEGMENTS OF THE TURING DEGREES

- Mathematics
- 2010

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.

### Local Initial Segments of The Turing Degrees

- MathematicsBulletin of Symbolic Logic
- 2003

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…

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

- Mathematics, PhilosophyThe Journal of Symbolic Logic
- 2009

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.

### Lattice initial segments of the turing degrees

- 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…

### Countable initial segments of the degrees of unsolvability

- MathematicsJournal 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.

### DENSITY OF A FINAL SEGMENT OF THE TRUTH-TABLE DEGREES

- Mathematics
- 1984

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…

### Continuous Lattices and Domains

- 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…

### The Theory of the Degrees below 0

- Philosophy
- 1981

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…

### On homogeneity and definability in the first-order theory of the Turing degrees

- MathematicsJournal 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…