In computability theory, a **Turing degree** is a measure of the level of non-computability of sets of natural numbers (or, more generally, of decision problems). It is a way to classify problems based on their inherent difficulty in terms of solutions that can be obtained by a Turing machine.
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The Turing degree of a set is its equivalence class under mutual Turing reducibility. Degrees inherit the partial order induced by Turing reducibility. The Friedberg–Muchnik theorem gives incomparable degrees represented by computably enumerable sets.