In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is 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. Wikipedia