## There is no degree invariant half-jump

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- by Rodney G. Downey and Richard A. Shore PDF
- Proc. Amer. Math. Soc.
**125**(1997), 3033-3037 Request permission

## Abstract:

We prove that there is no degree invariant solution to Post’s problem that always gives an intermediate degree. In fact, assuming definable determinacy, if $W$ is any definable operator on degrees such that $\mathbf {a} < W(\mathbf {a}) < \mathbf {a}’$ on a cone then $W$ is low$_2$ or high$_2$ on a cone of degrees, i.e., there is a degree $\mathbf {c}$ such that $W(\mathbf {a})'' = \mathbf {a}''$ for every $\mathbf {a} \geq \mathbf {c}$ or $W(\mathbf {a})'' = \mathbf {a}''’$ for every $\mathbf {a} \geq \mathbf {c}$.## References

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## Additional Information

**Rodney G. Downey**- Affiliation: Department of Mathematics, Victoria University of Wellington, P. O. Box 600, Wellington, New Zealand
- MR Author ID: 59535
- Email: rod.downey@vuw.ac.nz
**Richard A. Shore**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 161135
- Email: shore@math.cornell.edu
- Received by editor(s): February 16, 1996
- Received by editor(s) in revised form: May 9, 1996
- Additional Notes: The first author’s research was partially supported by the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell University Contract DAAL03-91-C-0027, the IGC of Victoria University and the Marsden Fund for Basic Science under grant VIC-509.

The second author’s research was partially supported by NSF Grant DMS-9503503 and the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell University Contract DAAL03-91-C-0027. - Communicated by: Andreas R. Blass
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 3033-3037 - MSC (1991): Primary 03D25, 03E60, 04A15; Secondary 03D30
- DOI: https://doi.org/10.1090/S0002-9939-97-03915-4
- MathSciNet review: 1401736