Thanks for the fun rabbit hole. They can’t really solve the halting problem though, you can make an oracle solve the halting problem for a turning machine but not for itself. Then of course you can make another oracle machine that solves the halting problem for that oracle machine, and so on and so forth, but an oracle machine can never solve its own halting problem.
Wait till you hear about oracle machines. They can solve any problem, even the halting problem.
(It’s just another mathematical construct that you can do cool things with to prove certain things)
Thanks for the fun rabbit hole. They can’t really solve the halting problem though, you can make an oracle solve the halting problem for a turning machine but not for itself. Then of course you can make another oracle machine that solves the halting problem for that oracle machine, and so on and so forth, but an oracle machine can never solve its own halting problem.