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High (computability)

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In computability theory, a Turing degree [X] is high if it is computable in 0, and the Turing jump [X] is 0, which is the greatest possible degree in terms of Turing reducibility for the jump of a set which is computable in 0.[1]

Similarly, a degree is high n if its n'th jump is the (n+1)'st jump of 0. Even more generally, a degree d is generalized high n if its n'th jump is the n'th jump of the join of d with 0.

See also

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References

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  1. ^ Soare, R. I. (1987). Recursively enumerable sets and degrees : a study of computable functions and computably generated sets. Berlin: Springer-Verlag. p. 71. ISBN 3-540-15299-7.