Good day,
I would love to ask this question. Lets have a hypercomputer capable of doing a hypertask, that is performing uncountably many computational steps in finite time(the same amount of steps as is the cardinality of a set of all real numbers). Let this hypercomputer also be able to work with data of a uncountable length. Also let this machine also be able to perform all basic operations which a turing machine could.
Now such a hypercomputer wouldn´t of course be able to solve it´s own halting problem, but, and this is the question here, would this machine be able to solve all algorithmicaly undecidable problems below its own halting problem, that is halting problem of a turing machine and arithmetical hierarchy, Analytical hierarchy and beyond up to but not including it´s own halting problem?
Thank you for your answer, I really hope that this question isn´t too vague as I have tried to be as specific as possible.
Have a nice day.