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  "body": "\n## Summary\n\nThe Turing degree of a set of natural numbers is the class of all sets that are Turing equivalent to it.\nTwo sets have the same degree when each is computable from the other, so the degree measures how uncomputable a set is.\nThe degrees are partially ordered by [[Turing reducibility|PA4PYQ1PZ0]], and the study of this order is a central part of computability theory.\n\n## Explanations\n\n### L1 human\n\nGroup sets of numbers by how hard they are to compute, where two sets are equally hard if each can be computed with the help of the other.\nEach group is a Turing degree.\nThe lowest degree, written $\\mathbf{0}$, contains all computable sets, such as the even numbers or the primes.\nThe set of halting programs lies in a higher degree, written $\\mathbf{0}'$.\nThe degrees form a large and intricate ordering, with uncountably many degrees and many incomparable pairs.\n",
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