# Ackermann ordinal

The smaller Ackermann ordinal is the limit of a system of ordinal notations invented by Ackermann (1951), and is sometimes denoted by $\phi_{{\Omega^2}}(0)$ or $\theta(\Omega^2)$ or $\psi(\Omega^{\Omega^2})$. Ackermann's system of notation is weaker than the system introduced much earlier by Veblen (1908), which he seems to have been unaware of.