The homogeneity conjecture
Copyright policy )The homogeneity conjecture
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.
- Cornell University United States
relative computability, Other degrees and reducibilities in computability and recursion theory, isomorphisms of cones of degrees, Turing degrees, degrees of unsolvability, homogeneity conjecture, Turing reducibility
relative computability, Other degrees and reducibilities in computability and recursion theory, isomorphisms of cones of degrees, Turing degrees, degrees of unsolvability, homogeneity conjecture, Turing reducibility
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