But we can do this for systems far beyond Peano's axioms. For example, the proof-theoretic strength of Kripke–Platek set theory is the Bachmann–Howard ordinal, and, in fact, merely adding to Peano's axioms the axioms that state the well-ordering of all ordinals below the Bachmann–Howard ordinal is sufficient to obtain all arithmetical consequences of Kripke–Platek set theory.
