High Quality Content by WIKIPEDIA articles! In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is intuitively described as an operation that assigns to each decision problem X a successively harder decision problem X? with the property that X? is not decidable by an oracle machine with an oracle for X. The operator is called a jump operator because it increases the Turing degree of the problem X. That is, the problem X? is not Turing reducible to X. Post's theorem establishes a relationship between the Turing jump operator and the arithmetical hierarchy of sets of natural numbers.

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