How Much Can You Prove With Certain Axioms?

Set theory is about adding axioms to your theory. You want to ask, how much can you prove with certain axioms? And this lends itself to a hierarchy called large cardinal axiom. So if the basic one is kind of that the set of all natural numbers is a set that's now that it's called the axiom of infinity. Now let's add this kind of thing, but higher up. The reason they do it, i was told, is that some ten years ago, so there was a strike just before the exam period,. and the university ended up without exams rig so now they want everybody to write the examad.