MUH doesn’t imply the existence of halting oracles. Indeed, the Computable Universe Hypothesis is supposed to be an extension of the Mathematical Universe Hypothesis, but CUH says that halting oracles do not exist.
There may be several confusions happening here. First I’ve been using MUH to mean “ultimate ensemble theory” (i.e., the idea that the Level IV multiverse of all mathematical structures exists), because Wikipedia says MUH is “also known as the ultimate ensemble theory”. But Tegmark currently defines MUH as “Our external physical reality is a mathematical structure” which seems to be talking just about our particular universe and not saying that all mathematical structures exist. Second if by “MUH doesn’t imply the existence of halting oracles” you mean that MUH doesn’t necessarily imply the existence of halting oracles in our universe, then I agree. What I meant in the OP is that the ultimate ensemble theory implies that universes containing halting oracles exist in the Level IV multiverse.
MUH doesn’t imply the existence of halting oracles. Indeed, the Computable Universe Hypothesis is supposed to be an extension of the Mathematical Universe Hypothesis, but CUH says that halting oracles do not exist.
There may be several confusions happening here. First I’ve been using MUH to mean “ultimate ensemble theory” (i.e., the idea that the Level IV multiverse of all mathematical structures exists), because Wikipedia says MUH is “also known as the ultimate ensemble theory”. But Tegmark currently defines MUH as “Our external physical reality is a mathematical structure” which seems to be talking just about our particular universe and not saying that all mathematical structures exist. Second if by “MUH doesn’t imply the existence of halting oracles” you mean that MUH doesn’t necessarily imply the existence of halting oracles in our universe, then I agree. What I meant in the OP is that the ultimate ensemble theory implies that universes containing halting oracles exist in the Level IV multiverse.
Hopefully that clarifies things?
OK, that makes sense.