User blog comment:P進大好きbot/Proposal to Choose an Official Standard OCF in This Wiki/@comment-11227630-20191219030804/@comment-11227630-20191219085432

Rathjen's OCF for Π3-reflection is stronger and complicated than Taranovsky's Degrees of Recursive Inaccessibility, with "+", "φ", "Ω", "Ξ" and "K". Rathjen's OCF is tricky, and it constructs ordinal Ψξπ(α) from larger π, so a large ordinal "K" is necessary (maybe so as "Ξ"). Rathjen's OCF do not naturally handle addition, so "+" is necessary. But I still cannot see the necessity of "φ" and "Ω", which can be naturally handled by both Ψ and C.

Can you point out the necessity of "φ" and "Ω" in Rathjen's OCF of Π3-reflection?