Ackermann ordinal

In mathematics, the Ackermann ordinal is a certain large countable ordinal, named after Wilhelm Ackermann. The term "Ackermann ordinal" is also occasionally used for the small Veblen ordinal, a somewhat larger ordinal.

There is no standard notation for ordinals beyond the

The smaller Ackermann ordinal is the limit of a system of ordinal notations invented by Ackermann (1951), and is sometimes denoted by ${\displaystyle \varphi _{\Omega ^{2}}(0)}$ or ${\displaystyle \theta (\Omega ^{2})}$, ${\displaystyle \psi (\Omega ^{\Omega ^{2}})}$, or ${\displaystyle \varphi (1,0,0,0)}$, where Ω is the

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