The homogeneity conjecture.

@article{Shore1979TheHC,
  title={The homogeneity conjecture.},
  author={Richard A. Shore},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1979},
  volume={76 9},
  pages={4218-9}
}
  • Richard A. Shore
  • Published 1979 in
    Proceedings of the National Academy of Sciences…
We show that, for any function f in which Kleene's O is computable, the ordering of Turning degrees (i.e., degrees of difficulty of computation of functions) is not isomorphic to the ordering of degrees of functions from which f is computable. This refutes a well-known conjecture of H. Rogers, Jr., and others.