User blog comment:Tetramur/Pentational arrays and beyond - comparisons/@comment-37993808-20200108154849/@comment-35470197-20200109011031

Thank you for the detail. But the finiteness of each process is not related to the infiniteness of the structure, and it does not mean the compatibility of two methods. For an elementary example, n→f_{ω↑↑ω}(n) (with respect to any reasonable choice of fundamental sequences) never coincides with n→f_{n↑↑n}(n). Your explanation looks similar to the statement that they coincide with each other because they have the same shape of the infinite structure. (Well, it is just my intuitive opininon, and is not directly explaining the issue on your explanation. Sorry if the example is not suitable.)

If I am correct, your explanation looks incompatible with Plain'N'Simple's explanation on Saibian's method. Is there a possibility that you and Plain'N'Simple refer to distinct formalisations by Saibian? Please tell me the source of Saibian's formalisation which you referred to.