 The rather famous ordinal that emerged in Gentzen’s consistency proof of PA is denoted by \(\varepsilon_0\). It refers to first ordinal \(\alpha&gt;0\) such that \((\forall \beta&lt;\alpha)\,\omega^{\beta}&lt;\alpha\). \(\varepsilon_0\) can also be described as the least ordinal \(\alpha\) such that \(\omega^{\alpha}=\alpha\).