User blog comment:KthulhuHimself/Terminal array notation./@comment-26428969-20151027080724/@comment-26428969-20151027133913

it is a susbsystem of second-order arithmetic. its proof-theoritic ordinal is $$\psi_{\Omega_1}(\Omega_\omega)$$, the supposed strength of BEAF's legion space in Hyp_cos's interpretation