Seminar: What is ... a large cardinal?
Abstract: Large cardinals appear in many contexts: e.g. as Grothendieck universes, they make life easier in category theory.
But this is just the start of a whole hierarchy of large cardinals! They can be used to measure the "consistency strength" of theories; allow us to derive new theorems about (comparatively) mundane structures such as the real numbers; and make our system of axioms more robust (e.g. by restraining the power of forcing to change the universe of set theory).
This lecture is part of the "What is..?" seminar.