be the set of Turing degrees of sets of natural numbers. Given some equivalence class , we may define the cone (or upward cone) of as the set of all Turing degrees such that ; that is, the set of Turing degrees that are "at least as complex" as under Turing reduction. In order-theoretic terms, the cone of is the upper set of .

Assuming the axiom of determinacy, the cone lemma states that if A is a set