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There has been a recent line of work on computable learnability: http://proceedings.mlr.press/v117/agarwal20b/agarwal20b.pdf http://www.learningtheory.org/colt2021/virtual/static/images/agarwal21b.pdf This seems to be exactly the sort of thing you're asking about. You also ask about the implications $1\implies 2$ and $2\implies 3$. The latter is indeed ...