Forum:SOA's ordinal

Is it correct that fundamental sequence for SOA's ordinal supposed to be $$\alpha[0] = 1$$ and $$\alpha[n+1] = C(\Omega^{\alpha[n]},0)$$ in Taranovsky's notation? If so, I guess that natural continuation of $$\psi(\Omega), \psi(M), \psi(K), \cdots$$ indeed might reach SOA (alternative guess is $$C(\Omega^{\Omega^\omega},0)$$). Ikosarakt1 (talk ^ contribs) 11:56, June 16, 2014 (UTC)