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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.
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.