 In this way, from the normal function f we get a two-place function, \(\varphi_{f} ( \alpha , \beta )\coloneqq f_{\alpha} ( \beta )\). One usually discusses the hierarchy when \(f=\ell\), where \(\ell( \alpha )=\omega^{\alpha}\). The least ordinal \(\gamma&gt;0\) closed under \(\varphi_{\ell}\), i.e., the least ordinal \(&gt;0\) satisfying \((\forall\alpha,\beta&lt;\gamma)\;\varphi_{\ell}(\alpha,\beta)&lt;\gamma\) is called \(\Gamma_0\). It has a somewhat iconic status, in particular since Feferman and Schütte determined it to be the least ordinal ‘unreachable’ by certain predicative means expressed in terms of autonomous progressions of theories (defined in  section 5.2).