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A random set which only computes strongly jump-traceable c.e. sets. (English) Zbl 1220.03042

Summary: We prove that there is a \(\Delta_2^0\), 1-random set \(Y\) such that every computably enumerable set which is computable from \(Y\) is strongly jump-traceable.
We also show that for every order function \(h\) there is an \(\omega \)-c.e. random set \(Y\) such that every computably enumerable set which is computable from \(Y\) is \(h\)-jump-traceable. This establishes a correspondence between rates of jump-traceability and computability from \(\omega \)-c.e. random sets.

MSC:

03D32 Algorithmic randomness and dimension
03D25 Recursively (computably) enumerable sets and degrees
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