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Up to n=2

Googol = 10^100 Googolplex = 10^10^100

Googolduplex = 10^Googolplex

Googoltriplex = 10^Googolduplex

Googolquadruplex = 10^Googoltriplex

Googol-n-plex = 10^Googol-(n-1)-plex

Up to n=3

Giggol = 10^^100

Giggoogol = 10^^10^100

Giggoogolplex = 10^^10^10^100

Giggoogol-n-plex = 10^^Googol-n-plex

Giggolplex = 10^^10^^100

Giggolduplex = 10^^Giggolplex

Giggoltriplex = 10^^Giggolduplex

Giggol-n-plex = 10^^Giggol-(n-1)-plex

Up to n=4

Gaggol = 10^^^100

Gaggoogol-n-plex = 10^^^Googol-n-plex

Gaggiggoogol-n-plex = 10^^^Giggoogol-n-plex

Gaggiggol-n-plex = 10^^^Giggol-n-plex

Gaggolplex = 10^^^10^^^100

Gaggolduplex = 10^^^Gaggolplex

Gaggoltriplex = 10^^^Gaggolduplex

Gaggol-n-plex = 10^^^Gaggol-(n-1)-plex

Up to n=w

Now, to make things easier, we will set a value n, which can have the value of any countable ordinal.

Now, we create the prefix for n, the number for n, and the active entry for x.

To solve (Number for n)-x-plex, change the active entry's value of the number for n to (Number for n)-(x-1)-plex.

To solve (Prefix for n)-x, change the active entry's value of the number for n to x.

Else, the active entry for the number for n has a value of 100. The active entry is represented with _.

n=1: Googol, Goo-, 10^_

n=2, Giggol, Gig-, 10^^_

n=3, Gaggol, Gag-, 10^^^_

n=4, Geegol, Gee-, 10^^^^_

n=5, Gigol, Gi-, 10{5}_

n=6, Goggol, Gog-, 10{6}_

n=7, Gagol, Ga-, 10{7}_

n=8, Goygol, Goy-, 10{8}_

n=9, Geggol, Geg-, 10{9}_

n=10, Guggol, Gug-, 10{10}_

Up to n=w2

n=w, Boogol, Boo-, 10{_}10

n=w+1, Corporal, Cor-, 10{{1}}_

Now, instead of using prefix for n, use x-into-(number for n)

n=w+2, Giggol-carta-Corporal, 10{{2}}_

n=w+3, Gaggol-carta-Corporal, 10{{3}}_

n=w+4, Geegol-carta-Corporal, 10{{4}}_

n=w+x, (Number for n=x)-carta-Corporal, 10{{x}}_

Up to n=w^2

Up to n=w^3

Up to n=w^w

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