Weaker Reductions
According to the Church-Turing thesis, a Turing reduction is the most general form of an effectively calculable reduction. Nevertheless, weaker reductions are also considered. A set A is said to be arithmetical in B if A is definable by a formula of Peano arithmetic with B as a parameter. The set A is hyperarithmetical in B if there is a recursive ordinal α such that A is computable from, the α-iterated Turing jump of B. The notion of relative constructibility is an important reducibility notion in set theory.
Read more about this topic: Turing Reduction
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