User blog:Ytosk/Continuing my TBMS

If you haven't seen my previous post about TBMS, here's the link: https://googology.wikia.org/wiki/User_blog:Ytosk/Transfinite_Extensions_of_BMS

The limit of the previous version of TBMS is (222...1 1 1). To solve this, i use superscripts. One thing that made this very strong is that n#=#n+11, where # can be any valid subscript that does not already contain m for any m>n. 1 does exactly what i talked about at the end of my previous post: it changes into a copy of the deepest which has that 1 in its subscript, and does not have anything in its superscript. Now we can define the limit of the previous TBMS, and some more examples:

(2211 1)=(222...1 1 1)

(2212 1)=(222...1211 211 1)

(2213 1)=(222...1212 212 1)

(2211,1 1)[n]=(221f(n) 1)[f(n)]

(22121 1)=(2212121... 1)

(22121,11 1)=(2212(2323123(...)31 1)21 1)

(221211 1)=(2212212...1 1 1)

(22111 1)=(22121...1 1 1)

(221(21121)11 1)=(221(21(21(...)11)11)11 1)

(221(211211,11)11 1)=(221(2112(211213(21121314(...)141)131)121)11 1)

(221(21121211 1)11 1)=(221(21121221(211212...1 1)11 1 1)11 1)

122 works similarly to 121, which is also known as 1, but 122 copies brackets with 1 in superscript, as in this example:

(221(2112121121221 1)11 1)=(221(211212112121121...1 1 1)11 1)

I will edit this page and add examples up to the limit of the current TBMS.