Are there any limitations that need to be placed on an oracle in order to maintain that the classical computability results (like the Halting Problem and the non-collapse of the arithmetic hierarchy) still hold in the relativized world? My textbook says that oracles can be uncomputable but I wasn't sure if that means they still need to be definable somehow in first-order arithmetic.
2026-03-25 09:50:51.1774432251
Limitations placed on an Oracle Turing Machine for Relativized Theorems
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