it is hard to conceive that questions about higher infinites that require infinitely many iterations of the Powerset operation can be relevant to physics.
If sets with cardinalities equal to these higher infinities exist as mathematical entities, then some of them will be logically dependent on us, on what we do. For example those sets may contain intelligent beings who are simulating our universe and taking different actions based on what they observe. I don’t know if this is actually the case, or if it is, how much we ought to care, but it would be nice if an FAI could consider and try to answer questions like this, and not be arbitrarily limited in its reasoning by the choice of mathematical language we make when building it.
If sets with cardinalities equal to these higher infinities exist as mathematical entities, then some of them will be logically dependent on us, on what we do. For example those sets may contain intelligent beings who are simulating our universe and taking different actions based on what they observe. I don’t know if this is actually the case, or if it is, how much we ought to care, but it would be nice if an FAI could consider and try to answer questions like this, and not be arbitrarily limited in its reasoning by the choice of mathematical language we make when building it.