[goldenkey]

The output of a program could be infinite and thus it never halts. Without Chatlin's constant or the Busy Beaver values, brute forcing is not feasible in a countably computable universe. It is still interesting to talk about Oracles, ie. Somehow getting hold of Chatlin's constant and thereby easily solving the halting problem and being able to use the induction.

[Strilanc]

These are easily fixed by dove tailing through the programs and using an increasing-over-time cutoff. Not fixed in the "made practical" sense, but in the "made non-contradictory" sense.

[goldenkey]

You can't use cutoffs. Timeouts deliver no guarantees within the universe of complexity.

[eli_gottlieb]

Solomonoff Induction starts by using Kolmogorov complexity to calculate its prior distribution, which already requires Chaitin's constant to be known.

So yeah.

[Strilanc]

Solomonoff induction goes from program to output to prediction weighted by program's length. It never goes from type of prediction to shortest equivalent program. It doesn't need to compute Kolmogorov complexities.

(Well, more specifically, approximations to it with time cutoffs don't have to compute Kolmogorov complexities. Raw Solomonoff induction already trivially runs into the halting problem.)