“Is impossible in our current world” carries the connotation of “contingently impossible”. If Omega is impossible because he can’t solve the Halting Problem, he’s necessarily impossible.
There may be prediction or undetectable coercion mechanisms that work on humans to make Omega able to predict/cause choices in such scenarios, which don’t require to a fully-general solution to halting.
“Is impossible in our current world” carries the connotation of “contingently impossible”. If Omega is impossible because he can’t solve the Halting Problem, he’s necessarily impossible.
There may be prediction or undetectable coercion mechanisms that work on humans to make Omega able to predict/cause choices in such scenarios, which don’t require to a fully-general solution to halting.