Can this be an official number on the wiki, with an article? It is named after me and my friend (Littlepeng9 didn't want any credit despite helping), since we helped come up with it. I am also considering naming it the Emlightened-Pellucid-Armstrong number, to reflect said poster'shelp. First we define the PPA (or EPA) Function as:
"The largest number defined by a formula φ, such that ZFC proves defines a unique number with a proof of length n"
And a proof of length n is defined as "n total applications of inference rules from the axioms of ZFC", using these rules and axiomization of ZFC: https://www1.maths.leeds.ac.uk/~rathjen/ICMend.pdf
Then the number is defined as PPA(Googolcentiplex)(Googolcentiplex), i.e. PPA of Googolcentiplex iterated
This number should be bigger than Fish Number 4 and possibly bigger than Xi(1,000,000), but smaller than Rayo's Number.