I've been reading about set theory and the difference between small and large cardinals. since taking the power set of small cardinals (alephs) allows us to create larger cardinals/alephs I know that an inaccessible cardinal is equivalent to the regular aleph fixed point, and cannot be reached by taking the power sets of alephs. So my questions are:
- what would the power set of an inaccessible cardinal be?
- what is the regular fixed point of the first inaccessible cardinal? (basically, a cardinal that is larger than the first inaccessible cardinal to the same degree the first inaccessible cardinal is larger than the first small cardinals like aleph 0)