High (computability)

{{Multiple issues| {{Notability|date=November 2021}} {{Technical|date=November 2021}} }} In computability theory, a Turing degree [''X''] is high if it is computable in 0{{prime}}, and the Turing jump [''{{prime|X}}''] is 0{{prime}}{{prime}}, which is the greatest possible degree in terms of Turing reducibility for the jump of a set which is computable in 0{{prime}}.<ref>{{cite book |last1=Soare |first1=R. I. |title=Recursively enumerable sets and degrees : a study of computable functions and computably generated sets |date=1987 |publisher=Springer-Verlag |location=Berlin |isbn=3-540-15299-7 |page=71}}</ref>

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{{prime}}.

==See also== * Low (computability)

== References == {{reflist}}

Category:Computability theory