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MrMind comments on Understanding and justifying Solomonoff induction - Less Wrong
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In the context of Bayesian reasoning, I understand "random" as "not enough information", which is different from "non-deterministic".
So that:
Only if we have enough information to exactly compute the next state from the previous ones. When this is not the case, lack of information acts as a source of randomness, for which SI can account.
In a sense, yes. There might still be useful pockets of computability inside the universe, though.
I'm not sure "higher-order" Solomonoff induction is even a thing.
"Higher-order" SI is just SI armed with an upgraded universal prior - one that is defined with reference to a universal hypercomputer instead of a universal Turing machine.
It's not that simple. There isn't a single model of hypercomputation, and even inside the same model hypercomputers might have different cardinal powers.