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This latter version has quite a bit of extra content, particularly at the end where he is discussing how far it is possible to push the game within different axiom systems. The discussion of his proof on why BB(8000) can't be determined within ZF set theory is also very interesting.

Thanks for pointing this out. He mentions in this one that he didn’t have time to get into Graham’s number, but I still think TREE(3) is worth mentioning.

Fun fact: The Kruskal Tree Theorem has been extended to undirected graphs (they form a quasi-wellordered set wrt the graph minor relationship), giving rise to an even faster growing sequence called the "Friedman's SSCG function".

The theorem is interesting for other reasons though: It allows us to define graph families by forbidding certain substructures.

>That essay might still get more views than any of the research I’ve done in all the years since.

Hey, it happened to Cicero, too!