Inherent enumerability of strong jump-traceability

Details Inherent enumerability of strong jump-traceability Inherent enumerability of strong jump-traceability

2011-10-07

arxiv.org/abs/1110.1435v1

Mathematics

Logic

25 pages

Scientific paper

We show that every strongly jump-traceable set obeys every benign cost function. Moreover, we show that every strongly jump-traceable set is computable from a computably enumerable strongly jump-traceable set. This allows us to generalise properties of c.e.\ strongly jump-traceable sets to all such sets. For example, the strongly jump-traceable sets induce an ideal in the Turing degrees; the strongly jump-traceable sets are precisely those that are computable from all superlow Martin-L\"{o}f random sets; the strongly jump-traceable sets are precisely those that are a base for $\text{Demuth}_{\text{BLR}}$-randomness; and strong jump-traceability is equivalent to strong superlowness.

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