User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191006023842/@comment-35470197-20191006040412

Of course. I was just curious what explicit assumptions you used. Taranovsky himself stated specific assumptions such as large cardinal axioms or the constructibility of the universe in his results including the well-foundedness, while you did not. Namely, Taranovsky has several reasonings other than intuitions on his results using set theory. What assumptions are you considering so that your results can be reasonablly guessed? (I am not requiring the proof. I am asking assumptions in set thoery.)