### Coherent randomness tests and computing the $K$-trivial sets

Laurent Bienvenu, Noam Greenberg, Antonín Kučera, André Nies, Dan Turetsky (2016)

Journal of the European Mathematical Society

Similarity:

We introduce Oberwolfach randomness, a notion within Demuth’s framework of statistical tests with moving components; here the components’ movement has to be coherent across levels. We show that a ML-random set computes all $K$-trivial sets if and only if it is not Oberwolfach random, and indeed that there is a $K$-trivial set which is not computable from any Oberwolfach random set. We show that Oberwolfach random sets satisfy effective versions of almost-everywhere theorems of analysis,...