I’m pretty comfortable working with strong axioms. But in terms of “would actually blow my mind if it turned out not to be consistent,” I guess alpha-inaccessible cardinals for any concrete alpha? Beyond that I don’t really know enough set theory to have my mind blown.
What’s the largest cardinal whose existence you feel comfortable with assuming as an axiom?
I’m pretty comfortable working with strong axioms. But in terms of “would actually blow my mind if it turned out not to be consistent,” I guess alpha-inaccessible cardinals for any concrete alpha? Beyond that I don’t really know enough set theory to have my mind blown.