Ambient control of the arithmetical hierarchy?

Responding to this: http://​​lesswrong.com/​​r/​​discussion/​​lw/​​8ys/​​a_way_of_specifying_utility_functions_for_udt/​​

I had a similar idea a few months ago that highlights different aspects of the problem which I find confusing. In my version the UDT agent controls bits of Chaitin’s constant instead of the universal prior directly, seeing as one of the programs that the oracle (which you can derive from Chaitin’s omega) has to solve the halting problem for is the UDT agent’s. But since the oracle for the oracle you get from Chaitin’s constant depends on the latter oracle’s bits, you seem to be able to ambiently control THE ENTIRE ARITHMETICAL HIERARCHY SAY WHAT!? That’s the confusing part; isn’t your one true oracle supposed to screen you off from higher oracles? Or is that only insofar as you can computably verify?

Anyway I like this theme of controlling computational contexts as it forms a tight loop between agent and environment, something currently lacking. Keep it up comrades!