Bachmann–Howard ordinal

In mathematics, the Bachmann–Howard ordinal (also known as the Howard ordinal, or Howard-Bachmann ordinal) is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such as Kripke–Platek set theory (with the axiom of infinity) and the system CZF of constructive set theory. It was introduced by Heinz Bachmann (1950) and William Alvin Howard (1972).

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