Some results on measure independent Gödel speed-ups
Martin K. Solomon · Journal of Symbolic Logic · 1978
Abstract We study the measure independent character of Gödel speed-up theorems, in particular, we strengthen Arbib's necessary condition for the occurrence of a Gödel speed-up [2, p. 13] to an equivalence result and generalize Di Paola's speed-up theorem [4]. We also characterize undecidable theories as precisely those theories which possess consistent measure independent Gödel speed-ups and show that a theory τ2 is a measure independent Gödel speed-up of a theory τ1 if and only if the set of undecidable sentences of τ1 which are provable in τ2 is not recursively enumerable.