User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180129200050/@comment-30118230-20180129222742

You have no idea how much I have to say here,but I will continue this discussion tomorrow since I have to go to bed.

As for the links:

http://web.mit.edu/dmytro/www/other/OrdinalNotation.htm#A6

http://web.mit.edu/dmytro/www/other/OrdinalNotation.htm#A6.2

The first link implies it's stronger than ZFC since it talks about theories like Z2 + PD,which is considerably stronger than ZFC and the second one directly states that the PTO of ZFC might be $$C(C(\Omega_2\omega,C(\Omega^{2}_2+\Omega_2,0)),0)$$ (note that these are just guesses and neither me nor Taranovsky have proofs for them.)

Again,I will continue this discussion tomorrow.