The paper is devoted to the study of the proof-theoretic strength of jump classes of the Turing degrees from the point of view of fragments of Peano arithmetic. It is shown that over the base theory PA\(^{-}\) + \(\Delta_{n}\)-induction, the existence of a non-trivial low\(_{n}\) Turing degree is equivalent to \(\Sigma_{n}\)-induction. This is done by investigating the jump of a \(\Sigma_{n}\) definable cut in a model of \(\Delta_{n}\)-induction.