Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4662016 | Annals of Pure and Applied Logic | 2012 | 11 Pages |
Abstract
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 23. To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than γ=log232, and a necessary condition is to have effective Hausdorff dimension greater than or equal to γγ.
► We show that our distribution is effectively equivalent to that of Cenzer et al. ► We study reals belonging to Martin-Löf random closed sets under such a distribution. ► We show that these reals all have high effective Hausdorff dimension. ► Conversely, they include all reals of sufficiently high effective Hausdorff dimension.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
David Diamondstone, Bjørn Kjos-Hanssen,