This does bring in the Berry paradox, since after all the hypothesis that the environment follows such a rule is in fact a very short hypothesis itself!
The resolution is that despite being describable by a short rule, it does not correspond to any computable program. Computing the results of any such hypothesis (even with the Solomonoff inductor requiring a Turing oracle already) would require an oracle of the next level up.
A super-Solomonoff inductor with a higher level Turing oracle can of course compute such a result and would assign it high weight in the described environment. Then that inductor likewise has short but uncomputable hypotheses, and so on.
This does bring in the Berry paradox, since after all the hypothesis that the environment follows such a rule is in fact a very short hypothesis itself!
The resolution is that despite being describable by a short rule, it does not correspond to any computable program. Computing the results of any such hypothesis (even with the Solomonoff inductor requiring a Turing oracle already) would require an oracle of the next level up.
A super-Solomonoff inductor with a higher level Turing oracle can of course compute such a result and would assign it high weight in the described environment. Then that inductor likewise has short but uncomputable hypotheses, and so on.