Your process of deciding what to do may at some point include simulating Omega and Omicron. If so, this means that when Omega and Omicron are simulating you, they are now trying to solve the Halting Problem. I am skeptical that Omega or Omicron can solve the Halting Problem.
They don’t need to solve the whole Halting Problem, for the same reason you don’t need to contradict Rice’s theorem if you had some proof (which I take as an axiom for the sake of the hypothetical) that the predictor was in fact perfect and that it is utility maximizing. Also, we can just try saying that there is a high probability that they will do this. Furthermore, you can imagine a restricted subset of Turing machines for which the Halting problem is computable. But also the only computers that exist in reality are really finite state machines.
Your process of deciding what to do may at some point include simulating Omega and Omicron. If so, this means that when Omega and Omicron are simulating you, they are now trying to solve the Halting Problem. I am skeptical that Omega or Omicron can solve the Halting Problem.
They don’t need to solve the whole Halting Problem, for the same reason you don’t need to contradict Rice’s theorem if you had some proof (which I take as an axiom for the sake of the hypothetical) that the predictor was in fact perfect and that it is utility maximizing. Also, we can just try saying that there is a high probability that they will do this. Furthermore, you can imagine a restricted subset of Turing machines for which the Halting problem is computable. But also the only computers that exist in reality are really finite state machines.