We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logarithm and Birkhoff's theorem. We also consider the hitting time operators, which share the Weihrauch degree of the former examples, but fail to be layerwise computable.
Given some set, how hard is it to construct a measure supported by it? We classify some variations of this task in the Weihrauch lattice. Particular attention is paid to Frostman measures on sets with positive Hausdorff dimension. As a side result, the Weihrauch degree of Hausdorff dimension itself is determined.
We study the Ramsey theoretic properties of combinatorial configurations which are generated by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.
We study partitions of Fra¨ıssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.