  Gödel stressed the fact that his approach to the problem of the continuum hypothesis was not constructive, since it needs the uncountable ordinal \(\omega_1\), and it was natural to study the ramified hierarchy along constructive ordinals. After preliminary works of Lorenzen and Wang, Schütte analysed what happens if we proceed in the following more constructive way. Since arithmetic has for ordinal strength \(\varepsilon_0\) we consider first the iteration of the ramified hierarchy up to \(\varepsilon_0\). Schütte computed the ordinal strength of the resulting system and found an ordinal strength \(u(1)\gt \varepsilon_0\). We iterate then ramified hierarchy up to this ordinal \(u(1)\) and get a system of ordinal strength \(u(2)\gt u(1)\), etc. Each \(u(k)\) can be computed in terms of the so-called Veblen hierarchy: \(u(k+1)\) is \(\phi_{u(k)}(0)\). The limit of this process gives an ordinal called \(\Gamma_0\): if we iterate the ramified hierarchy up to the ordinal \(\Gamma_0\) we get a system of ordinal strength \(\Gamma_0\). Such an ordinal was obtained independently about the same time by S. Feferman. It has been claimed that \(\Gamma_0\) plays for predicative systems a role similar to \(\varepsilon_0\) for Arithmetic. Recent proof-theoretical works however are concerned with systems having bigger proof-theoretical ordinals that can be considered predicative (see for instance Palmgren 1995).