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Squark comments on An additional problem with Solomonoff induction - Less Wrong
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The important property of SI is that it asymptotically produces correct predictions. I.e. if we fix an enumerable semi-measure and use it to (randomly) generate a sequence, SI will eventually start producing correct predictions with probability 1.
Consider the measure:
The measure is deterministic, but not computable. From SI point of view x is unpredictable (using the Universal prior). If we change the Universal prior of SI and base the prior on a Halting oracle instead of a universal Turing machine, m(x) becomes (hyper)computable. The question is - are there any conditions under which we should do this?
You are right, in principle we can consider generalized SI for various hypercomputation models. In practice, SI is supposed to be a probability distribution over "testable hypotheses". Since testing a hypothesis involves some sort of computation, it doesn't seem to make sense to include uncomputable oracles. It would make sense for agents that are able to hypercompute themselves.