How Far Can Infinity Go? Extreme Large Cardinals Explained

An introduction to the extreme upper reaches of large-cardinal set theory. The video constructs the cumulative hierarchy \(V_\alpha\), elementary embeddings, critical points and critical sequences from first principles, then develops the rank-into-rank axioms I3, I2, I1 and I0. It concludes with Kunen inconsistency, Reinhardt and Berkeley cardinals, rank-Berkeley cardinals, exacting and ultraexacting cardinals, and their relationships with the Axiom of Choice and HOD.