arXiv subjects
Publications and source records attributed to David Diamondstone.
The members of Martin-Löf random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-Löf random Galton--Watson trees with survival parameter $\frac{2}{3}$. To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than $γ=\log_2 \frac{3}{2}$, and a necessary condition is to have effective Hausdorff dimension greater than or equal to $γ$.
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-Löf 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.