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  "body": "\n## Summary\n\nThe Turing jump of a set $A$ of natural numbers is the halting problem for [[oracle machines|Z5CCVBME2V]] with oracle $A$.\nIt produces from $A$ a set $A'$ that is strictly harder than $A$ in the sense of [[Turing reducibility|PA4PYQ1PZ0]].\nIterating the jump starting from the empty set gives the sets $\\emptyset', \\emptyset'', \\ldots$, which line up with the levels of the [[arithmetical hierarchy|7CVJCQKY41]].\n\n## Explanations\n\n### L1 human\n\nGive a computer access to a set $A$ as an oracle.\nEven then it cannot decide which of its own programs halt; that question is the jump $A'$.\nSo each set leads to a harder one, and there is no hardest set.\nFor the empty set, which gives the computer no help at all, the jump is the ordinary [[halting problem|Z7TN2B35B0]].\n",
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