a consistent guessing oracle rather than a halting oracle (which I theorize to be more powerful than a consistent guessing oracle).
This is correct. Or at least, the claim I’m interpreting this as is that there exist consistent guessing oracles that are strictly weaker than a halting oracle, and that claim is correct. Specifically, it follows from the low basis theorem that there are consistent guessing oracles that are low, meaning that access to a halting oracle makes it possible to tell whether any Turing machine with access to the consistent guessing oracle halts. In contrast, access to a halting oracle does not make it possible to tell whether any Turing machine with access to a halting oracle halts.
This is correct. Or at least, the claim I’m interpreting this as is that there exist consistent guessing oracles that are strictly weaker than a halting oracle, and that claim is correct. Specifically, it follows from the low basis theorem that there are consistent guessing oracles that are low, meaning that access to a halting oracle makes it possible to tell whether any Turing machine with access to the consistent guessing oracle halts. In contrast, access to a halting oracle does not make it possible to tell whether any Turing machine with access to a halting oracle halts.
Thanks, didn’t know about the low basis theorem.