Some results on measure independent gödel speed-ups

Journal of Symbolic Logic 43 (4):667-672 (1978)
We study the measure independent character of Godel speed-up theorems. In particular, we strengthen Arbib's necessary condition for the occurrence of a Godel 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 Godel speed-ups and show that a theory τ 2 is a measure independent Godel speed-up of a theory τ 1 if and only if the set of undecidable sentences of τ 1 which are provable in τ 2 is not recursively enumerable
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