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