Hypercomputation is a "cheat" that extends the capability of a Turing machine or quantum computer or cellular automaton by adding extra abilities. A standard method is "Oracle machines", Turing machines with an extra black box device that can be queried and give an output that normally would be uncomputable. For example, a halting oracle would tell the machine a bit encoding whether an input program would ever terminate. Such "hypercomputation" machines can calculate various forms of uncomputable outputs.
My questions are:
Is hypercomputation compatible with our laws of physics? What about other incomputable things like Russell's set (things which its result is not computable because it does not exist)? Or what about other uncomputable/illogical/impossible/non-existent/inconsistent things? Are there hypercomputational systems that could encode/compute them?
Thank you for your help