In computability theory, Godel's incompleteness theorem [1934] finds expression in the definition of the jump operator. Thus, the Priedberg [1957] jump inversion theorem completely characterises the scope of the Godel undecidability phenomenon within the Kleene-Post [1954] degree structure for classifying unsolvable problems.

Minimal degrees of unsolvability naturally arise as the structural counterpart of decision problems whose solutions are extremely specialised (their solution does not have any other nontrivial applications). Spector [1956] showed that minimal degrees exist, while Sacks [1961] constructed one below 0′.

The first result concerning the jumps of minimal degrees was due to Yates [1970], who obtained a low minimal degree as a corollary to his construction of a minimal m below any given nonzero computably enumerable (or r.e.) degree. A global characterisation of such jumps was provided by the Cooper [1973] jump inversion theorem, while in the same paper it was shown that such a theorem could not hold locally (there are no high minimal degrees). The intuition that minimal degrees are in a sense close to 0 (the degree of the computable sets) was reinforced by Jockusch and Posner [1978], who found that all minimal degrees are in fact generalised low2 This, with Sasso's [1974] construction of a non-low minimal degree below ό, supported Jockusch's conjecture (see Yates [1974], p.235) that the jumps of minimal degrees below ό can be characterised as those ό-REA degrees which are low over 0′.