User blog comment:Alemagno12/Strength Level System/@comment-25337554-20151025060644/@comment-26428969-20151025093136

φ could be SVO -> LVO. then we need to do LVO -> BHO, BHO -> TFB, TFB -> psi(psi_I(0)), and after maybe "beyond psi(psi_I(0)), but still provably recursive in second-order arithmetic", then go to ZFC, and then "faster computable functions". I don't think we need more than one symbol for fast uncomputable functions