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Martin-Löf randomness and other randomness notions arising from computable tests; as well as related concepts such as Kolmogorov complexity, K-triviality, and effective Hausdorff dimension.
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Does the set of infinite random strings satisfy an analogue of immune sets?
In DST, the analogue would be having empty interior. The generalization of r.e. sets to the Polish setting is $\Sigma^0_1$ sets, which are recursively enumerable unions of open sets in our effective …