The proof-theoretic ordinal of a logical theory

Ordinal analysis seeks to determine the strength of a logical theory by assigning an ordinal to it.  Which one?  In this episode I describe a definition of the proof-theoretic ordinal of a logical theory from a paper by proof theorist Michael Rathjen.  It is basically a measure of how strong an induction principle is derivable in the theory.  (The first parts of the paper are pretty accessible, but the rest gets hard, at least for me.)