## Benign cost functions and lowness properties.(English)Zbl 1221.03036

In this paper the following interesting results are proved: 4.5mm
1.
A c.e. set $$A$$ is strongly jump-traceable if and only if it obeys all benign cost functions.
2.
For any benign cost function $$c$$, there is a c.e. set $$A$$ which obeys $$c$$ and is not strongly jump-traceable.
3.
Every strongly jump-traceable c.e. set is computable from any LR-hard random set.
4.
If a c.e. set is strongly jump-traceable, then it is computable from any $$\omega$$ -c.e. random set.

### MSC:

 03D25 Recursively (computably) enumerable sets and degrees 03D30 Other degrees and reducibilities in computability and recursion theory

### Keywords:

jump-traceable c.e. sets; c.e. random sets
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### References:

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